Physics Notes Xi

THE SCOPE OF PHYSICS CHAPTER # 1

QUESTIONS

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QUESTIONS

1994
Q.1 Q.8 (a) (a) Name three Muslim scientists? (3) Fill in the blanks:(1) (viii) The dimension of any physical quantity can always be expressed as some combination of the fundamental quantities.

1995
Q.1 (c) What are the dimensions of angular velocity “ω”? Show that the equation √ is (3) (1) dimensionally correct, where “T” is the time period of a simple pendulum of length “ ” at the place where acceleration due to gravity is “g”. Fill in the blanks:(v) Candela is the unit of intensity of light.

Q.8

(a)

1996
Q.1 (a) (i) Fill in the blanks:* Pinhole camera was designed by Ibn-ul-Haitam. * The basic unit of luminous body is candela (Cd). (2)

1998
Q.1 (a) (i) (ii) Q.1 (a) Give the names of three Muslim scientists who made remarkable contributions in the field of Physics. The S.I unit of Luminous intensity is candela (Cd). (2)

2000
State True or False for the following statements:(i) Kitab-ul- Manazir was written by Al-Razi. (ii) Thermodynamic unit of temperature is kelvin. (2) (F) (T) (2) Ibn-ul-Haitam * * (2) Ibn-e-Sina

2001
Q.1 (a) Choose the correct answer from the given options:(i) Laws of reflection and refraction are given by ___. * AL-Razi * Al-Beruni * (iii) The dimensions of angular Momentum is ___. * * * Show that the following equations are dimensionally correct:(i) Hint:√ , ,, , ,√ √ , -

Q.1

(c)

Page 1 of 111 “All Science Is Either Physics Or Stamp Collecting” Rutherford

THE SCOPE OF PHYSICS CHAPTER # 1

QUESTIONS

[e-mail]

√ √ ( ) ( ) Proved (ii) Hint:, , , , , , -

( )

Proved

2002 P/E
Q.1 (a) Choose the correct answer for each from the given options:(2) (i) The famous book on astronomy “Kitab-ul-Qanoon-ul-Masoodi” was written by ___. * Ibn-ul-Haitam * Abu-Rehan-al-Beruni * Ibn-e-Sina * Al-Khwarizmi (ii) The dimensions of angular velocity are ___. * * * *

2002 P/M
Q.1 (a) Q.2 (a) Select the correct answer for each from the given options:(1) (i) The famous book on astronomy “Kitab-ul-Qanoon-ul-Masoodi” was written by ___. * Al-Beruni * Al-Battani * AL-Masoodi * Al-Kindi Select the correct answer for each from the given options:(2) The dimensions of kinetic energy are ___. * * * * (iii) The number of Significant figures in are ___. * 2 * * 4 * 7

2003 P/E
Q.1 (a) Choose the correct answer for each from the given options:(i) Candela is the unit of ___. * Force * Luminous intensity * (ii) The dimensions of angular Momentum are ___. * * * (2) Mass * * (2) Velocity

2003 P/M
Q.1 (a) Select the correct answer for each from the given options:(i) For the quantity , the number of significant figures is ___. * 3 * 4 * * 7 (ii) The dimension of G are ___. * * *

* (1) * None of these (4)

2004
Q.1 (a) Q.1 (b) Select the correct answer for each from the given options:(i) The author of Al-Qanoon-Fit-Tib was ___. * Al-Razi * Ibn-e-Sina * Omer Khayyam Prove that the following equation are dimensionally correct:(i) Hint:“All Science Is Either Physics Or Stamp Collecting” Rutherford

Page 2 of 111

THE SCOPE OF PHYSICS CHAPTER # 1 [ ]

QUESTIONS , , [ ] )( ) ( ) Proved

[e-mail] , , -

, -

, -

(

)

( ( ( ) )

)

(

( )

(ii) Hint:-

√ , , , , √ √ √ √ ( ) , , -

( ) ( ) Proved

2005
Q.1 (a) Select the correct answer for each from the given options:(i) The number has ___ significant figures. * 3 * 4 * 5 * (iii) Which of the following was written by Ibn-ul-Haitam? * Kitab-ul-Manazir * Kitab-ul-Qanoon-ul-Masoodi * Kiatb-al-Shifa * Al-Qanoon-ul-Fit-Tib (2)

2006
Q.1 (a) Q.3 (a) Select the correct answer for each from the given options:(i) The number of significant figures in is ___. * * * * Choose the correct answer:(i) The dimensions of power is ___. * * (2)

* (1) * Al-Razi (1) * (1) Page 3 of 111

2007
Q.1 (a) Q.3 (a) Select the correct answer for each from the given options:(i) Kitab-ul-Manazir was written by ___. * Ibn-ul-Haitam * Al-Beruni * Ibn-e-Sina Select the correct answer for each from the given options:(ii) The basic unit of luminous intensity is ___. * * * Select the correct answer for each from the given options:(i) The dimensions of linear Momentum are ___. “All Science Is Either Physics Or Stamp Collecting” Rutherford

Q.4

(a)

THE SCOPE OF PHYSICS CHAPTER # 1 * Q.1 (a) *

QUESTIONS * *

[e-mail]

2008
Select the correct answer for each from the given options:(i) The author of book Al-Shifa was ___. * Al-Razi * Abu Rehan Al-Beruni * Ibn-e-Sina * Ibn-ul-Haitam (iii) The dimensions of torque are ___. * * * Select the correct answer for each from the given options:(i) The numbers of significant figures in 0.005040 is ___. * * * * (2)

* (1)

Q.2

(a)

2009
Q.1 Choose the correct answer for each from the given options:(i) Screw and lever were invented by ___. * Newton * Al-Farabi * Archimedes (xiv) The number of significant figures in is ___. * * * * (vi) The dimensions of kinetic energy are ___. * * * (3) * Galileo Galilei

*

2010
Q.1 Choose the correct answer for each from the given options:(i) The number of significant figures of is ___. * * * * (xvi) Kitabul-Manazir is written by ___. * Ibn-e-Sina * Ibn-ul-Haitam * (xvii) The dimensions of angular Momentum are ___. * * * (3)

Al-Razi *

*

Al-Beruni

2011
Q.1 Select the most appropriate answer for each from the given options:(vii) The dimensions of G are ___. * * * (xii) Light year is the unit of ___. * Time * Energy * Intensity (2) * * Distance (1)

2012
Q.1 Q.2 Select the most appropriate answer for each from the given options:(i) The product of two numbers and in the prospective significant number is ___. * * * * (ii) Give the dimensions of the following quantities :(a) Torque (b) Angular momentum (c) Pressure (d) K.E. (a) Torque ( ) Hint:- Torque is given as , , , , ( (b) , ) , ( ) (4)

Angular momentum Hint:- Angular momentum is given as

(

) Page 4 of 111

“All Science Is Either Physics Or Stamp Collecting” Rutherford

THE SCOPE OF PHYSICS CHAPTER # 1

QUESTIONS , , ( , ) , ( ) , -

[e-mail] , -

(c)

Pressure Hint:- Pressure is given as , , , , , , -

(d)

K.E. Hint:- Kinetic Energy is given as , , , , -

(

) ( ) ( )

Page 5 of 111 “All Science Is Either Physics Or Stamp Collecting” Rutherford

SCALARS &VECTORS CHAPTER # 2

QUESTIONS

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QUESTIONS

1992
Q.1 Q.1 (a) (c) Define Scalar product of two vectors. What are the properties of Scalar product? Give at least one example of Scalar product? (1+3+1) Fill in blanks with the correct answer chosen from the brackets:(6) (i) If a null or___ is multiplied by any finite number it gives a zero vector. (Unit vector, Zero vector) (ii) If a vector is divided by its magnitude, a ___ vector is obtained. (Zero, Unit) (iii) The component of a vector is the ___ value in a given direction. (Effective, Ineffective) (iv) Torque is the vector product of displacement vector and ___ vector. (Momentum, Force)

1993
Q.1 Q.1 (a) (b) What are Vector and Scalar quantities? (2) Two forces ⃗⃗⃗⃗ and ⃗⃗⃗⃗ are acting at a point making an angle “θ”. Assuming that vector ⃗⃗⃗⃗ is along X-axis, find the magnitude and direction of the resultant force by resolving them in to their Rectangular components. (5)

1994
ARI F RAZA

Q.1 Q.8 Q.8

(a) (a) (c)

Explain Commutative and Distributive laws for Dot product? Fill in the blanks:(i) A vector in any given direction whose magnitude is one is called a Unit vector. Choose the correct answer for each from the given options:(i) If ⃗⃗ and ⃗⃗ are two vectors, which of the following is correct? ⃗⃗ ⃗⃗ ⃗⃗ ⃗⃗ ⃗ ⃗ ⃗ * * *

(5) (1) (1) ⃗

1995
Q.1 (a) Q.1 Q.8 Q.8 (a) (c) (c) Define Vector product of two vectors. If vector ⃗⃗ and ⃗⃗ are inclined at angle “θ” with respect to each other, show that (⃗⃗ ⃗⃗ ) (⃗⃗ ⃗⃗ ). (2+4) OR Describe the addition of vectors by Rectangular-Components method. (6) Write down whether the following statement is True or False:(1) (xi) A Free vector is the one which can change its direction. (F) Choose the correct answer for each from the given options:(1) ⃗⃗ and ⃗⃗ ⃗⃗ ⃗⃗ then ___. (xxi) If ⃗⃗ ⃗⃗ ⃗⃗ & ⃗⃗ are parallel to each other * ⃗⃗ & ⃗⃗ are perpendicular to each other * * At least ⃗⃗ or ⃗⃗ is a null vector

1996
Q.1 (a) (ii) Choose the correct answer for each from the given options:(2) ⃗⃗ and ⃗⃗ are two vectors, then ___. (1) If ⃗⃗ ⃗⃗ ⃗⃗ ⃗⃗ ⃗ ⃗ ⃗ ⃗ * * * (2) If the vector addition of two vectors of magnitude and has a resultant of , then the angle between these two vectors is ___. * * * Using the definition of Vector product, prove the “Law of Sines” for a plane triangle of sides a, b & c. (6) Describe any two of following:(6) (iv) Addition of vectors by Rectangular-Components method. Page 6 of 111 “The Most Incomprehensible About The Universe Is That It Is Comprehensible” Einstein

Q.1 Q.4

(b) (c)

SCALARS &VECTORS CHAPTER # 2

QUESTIONS

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1997
Q.1 (a) Q.1 (b) Select the correct answer from the given possible answer:(i) If ⃗⃗ and ⃗⃗ are two vectors, which of the following is correct? ⃗⃗ ⃗⃗ ⃗⃗ ⃗⃗ ⃗ ⃗ * * Define:(i) Unit vector; (ii) Null vector. (1) * ⃗ ⃗ (2)

1998
Q.1 (a) Q.1 Q.1 Q.1 (b) (a) (b) Choose the correct answer from the given options:(i) If ⃗⃗ and ⃗⃗ are two vectors, which of the following is correct? ⃗⃗ ⃗⃗ ⃗⃗ ⃗⃗ ⃗ ⃗ * * Describe the addition of Vectors by Rectangular-Components method. (1) * ⃗ ⃗ (6)

1999
Fill in the blank with the correct answer:(1) (i) A vector in any given direction whose magnitude is one is called a Unit vector. (i) What are the Dot product and Cross products? Give their properties and examples. (1+1+1+1) (ii) Prove that:(3) ⃗⃗ ⃗⃗ ⃗⃗ ⃗⃗ ⃗⃗ (⃗⃗ ⃗ ) ⃗⃗ ⃗⃗ ⃗⃗ ⃗ (i) (ii) (⃗⃗ ⃗⃗ ) (⃗⃗ ⃗⃗ ) (iii)

2000
ARI F RAZA

Q.1

(a)

Q.1

(b)

State True or False for the following statements:(2) (iii) Null vector acts in a particular direction. (F) (iv) Dot product of two unit vectors acting along same direction is zero. (F) ⃗⃗⃗⃗ & ⃗⃗⃗⃗ are two vectors which acts at a point and make angles “θ1”& “θ2” respectively with X(i) axis. Find an expression only for the magnitude of their resultant using Rectangular-Components method. (6) (ii) If ⃗⃗ & ⃗⃗ represents the adjacent sides of a parallelogram then show that |⃗⃗ ⃗⃗ | represents area of the parallelogram. (3)

2001
Q.1 (a) Q.1 Q.1 (b) (a) Choose the correct answer from the given options:̂ ( ̂ ) has value ___. ̂ (ii) * * * ̂ * Define Scalar product of two vectors and show that ⃗⃗ (⃗⃗ (1) ̂ ⃗⃗ ⃗) ⃗⃗ ⃗⃗ ⃗ (1+4)

2002P/E
Q.1 (c) Choose the correct answer for each from the given options:(1) ̂ (i) The magnitude of product ̂ ( ̂ ) is ___. * * * * Explain the addition of two vectors by Rectangular-Components method. Calculate the resultant force. (5)

2002P/M
Q.1 Q.3 (c) (a) Show that (⃗⃗ ⃗⃗ ) (⃗⃗ ⃗⃗ ) Select the correct answer for each from the given options:̂ ̂ is equal to ___. (i) * ̂ * ̂ * * (3) (1)

2003P/E
Page 7 of 111 “The Most Incomprehensible About The Universe Is That It Is Comprehensible” Einstein

SCALARS &VECTORS CHAPTER # 2 Q.1 (a)

QUESTIONS Choose the correct answer for each from the given options:(iii) If two forces of same magnitude | | makes an angle of ___. * * * * Show that:⃗⃗ (⃗⃗ ⃗ ) ⃗⃗ ⃗⃗ ⃗⃗ ⃗

[e-mail] (1) with each other, their resultant is

Q.1

(b)

(4)

2003P/M
Q.1 (a) Q.1 Q.2 (c) (a) Select the correct answer for each from the given options:(1) (iii) If a vector quantity is divided by its magnitude the vector obtained is called ___. * Unit vector * Position vector * Null vector * Free vector Define Vector product of two vectors and show that:(1+4) (⃗⃗ ⃗⃗ ) (⃗⃗ ⃗⃗ ) Select the correct answer for each from the given options:(1) (iii) The Dot product of unit vectors ̂ ̂ is ___. * * * * ̂

2004
Q.1 (a) Select the correct answer for each from the given options:(2) ⃗⃗ , when ⃗ 0, ⃗ 0, then the vectors are ___. (ii) If ⃗ ⃗ * Parallel * Opposite * Perpendicular * None of these ⃗| | ⃗ |, the angle between the vectors ⃗⃗ ⃗⃗ is ___. (iii) When | * * * How many methods of addition of vectors are given in your book? Write their names. Describe the addition of two vectors ⃗⃗ 1 & ⃗⃗ 2 , making angle “θ1”& “θ2” with + ve X-axis respectively by RectangularComponents method. (1+3)
ARI F RAZA

Q.1

(c)

2005
Q.1 (a) Q.1 Q.1 (b) (c) Select the correct answer for each from the given options:(1) ⃗⃗ and ⃗⃗ ⃗⃗ ⃗⃗ and ⃗⃗ (ii) If ⃗⃗ ⃗⃗ , then vector ⃗⃗ is ___. * Equal to ⃗⃗ * Zero * Perpendicular to ⃗⃗ * Parallel to ⃗⃗ Define the following:(3) (i) Unit vector; (ii) Position vector; (iii) Free vector. Explain Cross-product of two vectors. Show that the magnitude of the Vector product gives the area of the parallelogram whose adjacent sides are represented by the two vectors. (3+2)

2006
Q.1 (a) Q.1 Q.1 (b) (a) Select the correct answer for each from the given options:̂ ( ̂ ) is equal to ___. ̂ (iii) ̂ * * * ̂ * Describe the addition of two vectors by Rectangular-Components method. (1) (4) (1) ⃗ (2+2) (2) * Momentum Page 8 of 111 “The Most Incomprehensible About The Universe Is That It Is Comprehensible” Einstein

2007
Select the correct answer for each from the given options:(ii) The area of a parallelogram formed by two vectors ⃗⃗ & ⃗⃗ is given by ___. ⃗ ⃗| ⃗| * * | * | * Describe the Dot product of two vectors. Show that:⃗⃗ (⃗⃗ ⃗ ) ⃗⃗ ⃗⃗ ⃗⃗ ⃗ Select the correct answer for each from the given options:(i) The Dot product of Force & Velocity is ___. * Work * Power * Energy

Q.1 Q.3

(b) (a)

SCALARS &VECTORS CHAPTER # 2 (iii)

QUESTIONS

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A Vector which can be displaced parallel to itself and is applied at any point is known as ___ vector. * Null * Unit * Position * Free

2008
Q.1 (a) Select the correct answer for each from the given options:(1) (ii) Two perpendicular vectors having magnitudes & are added. Their resultant has the magnitude ___. * * * * Describe the addition of vectors by Rectangular-Components method. (4)

Q.1 Q.1

(b)

2009
Choose the correct answer for each from the given options:(3) (ii) If a vector is divided by its magnitude, the resulting vector is called ___. * Position vector * Unit vector * Null vector * Free vector (vii) Two perpendicular vectors having magnitudes of and are added. The resultant has the magnitude of ___. * * * * ̂ are the unit vectors along (xvi) If ̂ ̂ axes respectively, then ̂ ̂ ̂ * ̂ * * * (i) Can the magnitude of resultant of two vectors of the same magnitude be equal to the magnitude of either of the vectors? Give mathematical reasons for your answer. ⃗⃗⃗ ⃗⃗⃗ ⃗⃗⃗ ⃗⃗⃗ Ans. |⃗⃗⃗ | |⃗⃗⃗ | |⃗⃗⃗ ⃗⃗⃗ | |⃗⃗⃗ | |⃗⃗⃗ |
ARI F RAZA

Q.2

|⃗⃗⃗

⃗⃗⃗ | |⃗⃗⃗ | |⃗⃗⃗ | |⃗⃗⃗ | |⃗⃗⃗ | |⃗⃗⃗ | |⃗⃗⃗ | |⃗⃗⃗ | |⃗⃗⃗ |

√|⃗⃗⃗ | √|⃗⃗⃗ | √ |⃗⃗⃗ | (√ |⃗⃗⃗ | |⃗⃗⃗ | |⃗⃗⃗ | |⃗⃗⃗ |

|⃗⃗⃗ | |⃗⃗⃗ | |⃗⃗⃗ | |⃗⃗⃗ | |⃗⃗⃗ | |⃗⃗⃗ |

|⃗⃗⃗ ||⃗⃗⃗ | |⃗⃗⃗ ||⃗⃗⃗ | |⃗⃗⃗ | |⃗⃗⃗ | |⃗⃗⃗ ⃗⃗⃗ | |⃗⃗⃗ |

)

(

) ⃗⃗⃗⃗ ⃗⃗⃗⃗

Q.4

(a)

Define the Cross-product of two vectors. Show that the Cross-product does not obey Commutative law. Also prove that :- ⃗⃗ (⃗⃗ ⃗ ) ⃗⃗ ⃗⃗ ⃗⃗ ⃗ (1+3+3)

2010
Q.1 Choose the correct answer for each from the given options:⃗⃗ and ⃗⃗ ⃗⃗ ⃗⃗ and ⃗⃗ (xiv) If ⃗⃗ ⃗⃗ , then vector ⃗⃗ is ___. * Equal to ⃗⃗ * Zero * Perpendicular to ⃗⃗ (1) * Parallel to ⃗⃗ Page 9 of 111 “The Most Incomprehensible About The Universe Is That It Is Comprehensible” Einstein

SCALARS &VECTORS CHAPTER # 2 Q.4 (b)

QUESTIONS

[e-mail]

Show that the Cross-product of a vector is not commutative (⃗⃗ ⃗⃗ ) (⃗⃗ ⃗⃗ ) and prove that the magnitude of the Cross-product of two vectors gives the area of the parallelogram. (4+3)

2011
Q.1 Q.2 Select the most appropriate answer for each from the given options:(1) ⃗⃗ and ⃗⃗ ⃗⃗ ⃗⃗ and ⃗⃗ (ii) If ⃗⃗ ⃗⃗ , then vector ⃗⃗ is ___. * Equal to ⃗⃗ * Zero * Perpendicular to ⃗⃗ * Parallel to ⃗⃗ (iv) Can the magnitude of resultant of two vectors of the same magnitude be equal to the magnitude of either of the vectors? Explain mathematically. (4) Hint:- Same as Q.2 (i) 2009 (a) Two forces ⃗⃗⃗⃗ & ⃗⃗⃗⃗ are acting at a point and making angles “θ1”& “θ2” with positive x-axis respectively. Derive the expressions for the magnitude of the resultant force and its direction with respect to the positive x-axis. (7)

Q.5

2012
Q.1 Q.4 Select the most appropriate answer for each from the given options:⃗ is equal to ___. (vii) If ̂ and ⃗ ̂, then ̂̂ ̂̂ ⃗⃗ * * * * None of these (a) Define Scalar and Vector products, five one example of each. Show that:⃗⃗ ⃗⃗ ⃗⃗ ⃗⃗ ⃗⃗ (⃗⃗ ⃗ ) ⃗⃗ ⃗⃗ ⃗⃗ ⃗ (i) (ii)
ARI F RAZA

(1)

(3) (4)

Page 10 of 111 “The Most Incomprehensible About The Universe Is That It Is Comprehensible” Einstein

SCALARS &VECTORS CHAPTER # 2

GOVT DEGREE COLLEGE S.R.E MAJEED, STADIUM ROAD NUMERICALS

NUMERICALS
Q.1 Q.1 (b) Find the angle ( Hint:⃗⃗ ⃗ ̂ ̂ ) between the vectors ⃗⃗ and ⃗⃗ where ⃗⃗ ̂ ̂ , ⃗⃗⃗ ̂ ( ) ̂) ( ̂ ̂) ̂ ̂) ( ̂) ( ̂) ( ̂) ( ⃗ ⃗ ⃗ ⃗ ⃗ | | | | | | | | |⃗ | |⃗ | |⃗ | |⃗ | ( ) ( ) ( )( ) √( ) √ √ ( ) ( )
ARI F RAZA

̂

̂ & ⃗⃗⃗ ̂

| || ⃗ | | || ⃗ | ( ̂ ̂ ( ̂) ( ̂)

̂

̂,

̂. ̂ (4)

√( ) √ √

( )

(

)

Q.2

( 40.36 ) Q.1 (c)

1992 Two vectors of magnitude 10 units (| |) and 15 units (| ⃗ |) are acting at a point. The magnitude of ⃗ |); Find the angle ( their resultant is 20 units (| ) between them. (4) ⃗| Hint:- | | , |⃗ | ,| , | ( ⃗| ) √| | √( ) .√( ) |⃗ | ( ) ( ) | || ⃗ | ( )( ( ) )( ) /

( (75.5 )

) 1993 Page 11 of 111

“Truth Is Ever To Be Found In The Simplicity, And Not In The Multiplicity And Confusion Of Things.” Newton

SCALARS &VECTORS CHAPTER # 2 Q.3 Q.1 (d) If ⃗⃗ Find:(i) (vi) (ix) (i) (ii) (iii) (iv) (v) (vi) Hint:̂

GOVT DEGREE COLLEGE S.R.E MAJEED, STADIUM ROAD NUMERICALS ̂ and ⃗⃗ ̂ ⃗⃗⃗ - ⃗ ) of ⃗ on to ⃗ (v) (viii) (4) ⃗ ⃗ ⃗ ⃗

⃗ ⃗ |⃗ | (ii) |⃗ | (iii) (iv) ⃗ Angle ( ) between ⃗ (vii) Projection ( Unit vector perpendicular( ̂) to the plane of ⃗ and ⃗ |⃗ | Hint:|⃗ | Hint:⃗ + ⃗ Hint:⃗⃗⃗ - ⃗ Hint:⃗ ⃗ Hint:|⃗ | |⃗ | ⃗ ⃗ ⃗ ⃗ ⃗ ⃗ ⃗ ⃗ ̂ ( ̂ √( ) √( ) ( ̂ ( ) ( ) ̂) ̂ ̂) ̂ ̂ ̂ ̂ ̂ ̂ ( ̂ ̂) ( ( ) ̂ ) √ ̂ ̂ ̂ ̂ ( ) √ √

( )

| ⃗ || ⃗ | ⃗ ⃗ | ⃗ || ⃗ | ( )(√ ) ( )

ARI F RAZA

(vii) Hint:⃗ ⃗ | ⃗ || ⃗ | ⃗ ⃗ |⃗ | ⃗ ⃗ |⃗ | ⃗ ⃗ |⃗ |

⃗ ⃗

⃗ ⃗

(viii)

⃗

⃗ ⃗ ⃗ ⃗ ⃗ ⃗ ⃗ ⃗ ⃗ ⃗ ⃗ ̂ ̂ ̂ ( ̂ ̂ ̂ ̂ ̂) ̂ ̂ ̂ ̂ ( ̂ ̂ ̂) ̂ ̂

Hint:-

(ix)

̂ Hint:-

⃗ ⃗ |⃗ ⃗ ⃗| ( )

⃗

Page 12 of 111 “Truth Is Ever To Be Found In The Simplicity, And Not In The Multiplicity And Confusion Of Things.” Newton

SCALARS &VECTORS CHAPTER # 2

GOVT DEGREE COLLEGE S.R.E MAJEED, STADIUM ROAD NUMERICALS |⃗ |⃗ |⃗ |⃗ ⃗| ⃗| ⃗| ⃗| ( )̂ ̂ ̂ ̂ √ √ ̂ | | ⃗⃗⃗ ⃗⃗⃗ ⃗⃗⃗ |⃗⃗⃗ (ii) | | Hint:|⃗⃗⃗ | |⃗⃗⃗ | |⃗⃗⃗ | |⃗⃗⃗ | |⃗⃗⃗ | (iii) | Hint:⃗⃗⃗ ⃗⃗⃗ ⃗⃗⃗ ⃗⃗⃗ ̂ ̂ ̂ , ⃗⃗⃗⃗ ̂ (ii) √( ) √ √ √ ̂ √ ̂ √ √ ̂ ̂
√

( ) ̅̅̅̅̅̅̅ ̂

(

)

.√ Q.4 Q.1

̂ (c)

̂

̂ ̂ Given Find:(i) (i)

̂ ⃗⃗⃗⃗

̂ ̂

̂ ̂

√

̂/ ̂ | ̂) ̂ ̂ ( ) ) ̂ √ ̂ ̂ | ̂ )] ̂) √ (5)

̂ , ⃗⃗⃗⃗

| | Hint:-

| |

(iii) ̂) ̂ ̂
ARI F RAZA

⃗⃗⃗ ⃗⃗⃗ ⃗⃗⃗

⃗⃗⃗ ⃗⃗⃗ ⃗⃗⃗ ⃗⃗⃗

[( ̂ ( ̂ ̂ ⃗⃗⃗ |

) ̂

( ̂ ( ̂ ( )

( ̂ (̂

̂ ̂

̂

√( ) ( )

( ) √( ) √ √ √̅̅̅̅̅̅̅ √ | ⃗⃗⃗ ⃗⃗⃗ ⃗⃗⃗ ⃗⃗⃗ | ⃗⃗⃗

⃗⃗⃗ ⃗⃗⃗ ⃗⃗⃗ ⃗⃗⃗ ⃗⃗⃗

[ ( ̂ [( ̂ [( ̂ ̂ ̂ ⃗⃗⃗ |

̂ ̂ ̂ √(

̂) ̂) ̂) ̂ ) , |⃗⃗ |

( ̂ ( ̂ ( ̂ ̂ ( )

̂ ̂ ( ) ⃗⃗ |

̂) ̂)

( ̂ ( ̂ ̂) ( ̂ √

̂

̂ )] ̂ )] ̂ ̂ ̂ )] √ 1994

Q.5

(√ , √ , √ Q.1 (b)

) If two vectors ⃗⃗ and ⃗⃗ are such that |⃗⃗ | Find; ⃗ ⃗| (i) (ii) | Hint:- |⃗⃗ | |⃗⃗ | |⃗⃗ ⃗⃗ | (i) | | ⃗| ⃗| √( ) ( ) .√ ⃗ √| | √| | ( )

and |⃗⃗

(6) , |⃗ | |⃗ | ⃗ ⃗/ (i) ,| || ⃗ | ⃗ ⃗ ⃗ | || ⃗ | (ii) | ⃗|

Page 13 of 111 “Truth Is Ever To Be Found In The Simplicity, And Not In The Multiplicity And Confusion Of Things.” Newton

SCALARS &VECTORS CHAPTER # 2

GOVT DEGREE COLLEGE S.R.E MAJEED, STADIUM ROAD NUMERICALS ⃗ ⃗ ⃗⃗ ⃗⃗ (ii) | | | | ⃗| ⃗| ⃗| ⃗| √| | √( ) √ √ ⃗. ⃗⃗⃗ ⃗) |⃗ | ( ) ( ⃗ )

( Q.6 Q.1

√

) (d) If ⃗⃗⃗ ̂ ̂ ⃗⃗⃗ Hint:̂ ̂ ̂ ⃗ ⃗ ⃗ | | | ( )̂ ̂ ⃗| ⃗| ⃗| ̂ √ √ ̂ √ ̂ √ ̂ | ̂ , ⃗⃗⃗ ̂ ̂ ̂ , ⃗⃗⃗ ̂ . Find a unit vector parallel to ⃗⃗⃗ ̂, ̂ ̂ ̂ ( ⃗ ⃗ ( ) ⃗| ̂ )] [( ̂ ̂ ̂) ( ̂ ̂ ̂ ̂ )) (̂ ,( ̂ ̂ ̂) ( ̂ ̂ ̂ ̂
ARI F RAZA

(6)

√( √ √ ̂

)

( )

(

)

̂

(̂ Q.7 Q.1

√ (c)

̂

̂) ̂ √ √ Find the value of “p” for which the following vectors becomes perpendicular to each other. ̂ ̂ ⃗⃗⃗ ⃗⃗⃗ ̂ ̂ ̂ ̂ (5) ̂ , ⃗⃗⃗ ̂, ⃗⃗⃗ Hint:̂ ̂ ̂ ̂ ⃗ ⃗ ̂) ( ̂ ̂) (̂ ̂ ̂ ( ̂) ( ) ( ̂) ( ̂) ( ̂ ) ( ̂ ) ̂

Q.8

( Q.1

) (b)

1996 The magnitudes of two vectors are 4 (| |) and 5 units (| ⃗ |) and the angle between them is 30 ( ). Taking first vector on X-axis; Find the magnitude of resultant (| ⃗ | ) vector and its direction ( ). (6) ⃗| ⃗| , Hint:- | | ,| , ,| ⃗ ⃗

Page 14 of 111 “Truth Is Ever To Be Found In The Simplicity, And Not In The Multiplicity And Confusion Of Things.” Newton

SCALARS &VECTORS CHAPTER # 2 |⃗ |

GOVT DEGREE COLLEGE S.R.E MAJEED, STADIUM ROAD NUMERICALS √| | |⃗ | ( ) | || ⃗ | ( )( )

| ⃗ | √( ) |⃗| √ ⃗| √ | |⃗⃗ |

|⃗ | |⃗ | |⃗ |

|⃗|

( ( (b) ) ̂ ̂ ⃗|

) 1997

Q.9

Q.1

Given ⃗⃗⃗ Find:(i) | (i)

̂ and ⃗⃗⃗ ̂ (ii)

̂ ⃗
ARI F RAZA

̂. (iii) Angle ( ) between &⃗

(6)

⃗| | Hint:-

⃗ ⃗ ⃗ ⃗| ⃗| ⃗| ⃗ ⃗ ⃗ ⃗ ⃗

[ (̂ [( ̂ ̂ √ √ ̂ ̂ ̂ ̂ √( )

̂ ̂)

̂) ( ̂ ̂ ( )

( ̂ ̂) ( )

̂ )] ( ̂ ̂ )] ̂

| | | (ii) ⃗ Hint:-

(̂ |

̂

̂) |

( ̂ ̂|

̂ |

̂) ̂| ) | ̂| | ̂ ,( )( ) ( )( )-

,( )( ̂ , ̂ ̂

)

( )( )̂, ̂

̂,( )( - ̂,

( )( )-

(iii) Hint:(√ Q.10 Q.1 , (c) ̂ ̂ , Prove Hint:| ⃗| ( ) | ⃗| ( ⃗) | ⃗) ⃗| ( ⃗| *| || | | |⃗ | ⃗) + *| || ⃗ | | | |⃗ | ) | | |⃗ | + Same as Q.1 1997 (5)

| | |⃗ | ( | | |⃗ | ( )

1998 Page 15 of 111 “Truth Is Ever To Be Found In The Simplicity, And Not In The Multiplicity And Confusion Of Things.” Newton

SCALARS &VECTORS CHAPTER # 2 Q.11 Q.1 (c)

GOVT DEGREE COLLEGE S.R.E MAJEED, STADIUM ROAD NUMERICALS If one of the Rectangular components of a force of 100 N(| |) is 50 N(|⃗⃗⃗ |). Find the other component(|⃗⃗⃗ | )? (5) ⃗⃗⃗ | ⃗⃗⃗ | Hint:- | | ,| ,| |⃗⃗⃗ | |⃗⃗⃗ | | |

| |

√|⃗⃗⃗ | √(

|⃗⃗⃗ | ) (√( ) |⃗⃗⃗ | |⃗⃗⃗ | |⃗⃗⃗ | |⃗⃗⃗ | )

(

)

|⃗⃗⃗ | √|⃗⃗⃗ | |⃗⃗⃗ | Q.12 ( Q.1 ) (c)
ARI F RAZA

√ 1998

Determine a unit vector ( ̂ ) perpendicular to plane containing ⃗⃗ and ⃗⃗ if; ̂ ⃗⃗⃗ ̂ ̂ ̂ ⃗⃗⃗ = ̂ ̂ ̂, ̂ Hint:- ⃗⃗⃗ ̂ ̂ ̂ , ⃗⃗⃗ = ̂ ̂ ( ) ⃗ ̂ ⃗ ( ) ̂ ⃗| | ̂) ⃗ ( ̂ ̂ ̂) ( ̂ ̂ ̂ ̂ ̂ ⃗ | | ⃗ ⃗ ⃗ ⃗ ̂ √( √ √ ̂ √ √ ̂ √ ̂ √ ̂. ̂ Angle ( ) between ⃗⃗⃗ and ⃗⃗⃗ ̂ ̂ ̂ ) | | | ( )̂ ̂ ⃗| ⃗| ⃗| ̂| ,( ̂ , ̂ )( | ̂| | ̂| | )— ( )( ) ̂ [( )( )— ( )( )-

(6)

) ( )( )̂[( )( - ̂, ̂, ̂ ̂ ( ) ( )

Q.13

( √ Q.1

̂

√ (c)

̂

If ⃗⃗⃗ Find:(i)

√

̂) ̂ | ̂ ⃗| ̂ , ⃗⃗⃗ ̂ (ii)

(4) Page 16 of 111

“Truth Is Ever To Be Found In The Simplicity, And Not In The Multiplicity And Confusion Of Things.” Newton

SCALARS &VECTORS CHAPTER # 2 Hint:⃗⃗⃗

GOVT DEGREE COLLEGE S.R.E MAJEED, STADIUM ROAD NUMERICALS ̂ | | ⃗ ⃗ ⃗ ⃗ | | | | | | |⃗ | |⃗ | |⃗ | ( )| | (ii) ⃗| |⃗⃗ √ ⃗⃗ |
ARI F RAZA

̂

̂ , ⃗⃗⃗ ̂ ⃗| ⃗| √| | √| | ( ̂ ̂ ( ) ( ̂

̂ |⃗ | |⃗ |

̂,

(i) ( )

|

⃗|

(ii)

(i)

,| || ⃗ | ⃗ ̂

⃗

| || ⃗ |

̂) ( ̂ ̂) ( ̂) ( ̂)

̂) ̂) ( ̂) (

√( ) √ √ √( √ √ ⃗| √ )

( )

(

)

( )

( )

√(√

)

(√

)

(

)

Same as Q.1 2000 ) to ( ) when a uniform force ) and the angle ( ) between force and (5) ⃗⃗⃗ ⃗⃗⃗ ̂ ⃗⃗⃗ ⃗⃗⃗ ̂) ̂ ̂) ̂) ̂ ̂, ,

Q.14

(√ , Q.1

) (c) An object moves along a straight line from ( ̂ acts on it. Find the work done ( ⃗⃗⃗ ̂ ̂ displacement. Hint:⃗⃗⃗ ̂ (⃗⃗⃗ ( ̂ ̂ ̂ ⃗⃗⃗ ̂ ( ) ̂ ⃗⃗⃗ ) ̂ ̂,

⃗⃗⃗ ⃗⃗⃗

⃗⃗⃗

̂)

( ̂

̂ ⃗⃗⃗ ̂ ̂ ̂) ( ̂ ( ) ( ̂ ̂ ̂ ( ) ( ) ( ̂) ( ̂) ( ̂ ) ( ̂ ̂

| || | ( ) | || | ( ) ( ) √( ) √ √ √( √ ) ( ) ( )

| | | | | | | | | |

Page 17 of 111 “Truth Is Ever To Be Found In The Simplicity, And Not In The Multiplicity And Confusion Of Things.” Newton

SCALARS &VECTORS CHAPTER # 2 | | ( )

GOVT DEGREE COLLEGE S.R.E MAJEED, STADIUM ROAD NUMERICALS √ √ √ √ √

( ( Q.2 , (d)

)

Q.15

) 2001 ̂ and ⃗⃗⃗ ̂ . Find a unit vector( ̂) perpendicular to plane containing If ⃗⃗⃗ ̂ ̂ ̂ ̂ both ⃗⃗⃗ & ⃗⃗⃗ . If ⃗⃗⃗ and ⃗⃗⃗ forms the sides of a parallelogram, find the area ( ) of the parallelogram. (4) ̂ , ⃗⃗⃗ ̂, ̂ Hint:- ⃗⃗⃗ ̂ ̂ ̂ ̂ (i) ( ) (ii) ⃗ ⃗ ̂ (i) ⃗ ⃗ ( ) ̂ |⃗ ⃗ | ̂) ( ̂ ̂) ⃗ ⃗ ( ̂ ̂ ̂ ̂ ̂ ̂ ⃗ ⃗ | |
ARI F RAZA

⃗ ⃗ ⃗ ⃗ |⃗ |⃗ |⃗

⃗ ⃗ ⃗ ⃗ ⃗| ⃗| ⃗| ( )̂

̂| ,( ̂ ̂, √( √ √ ̂

| )( ) ̂ )

̂|

|

̂|

| ̂ [( )( )— ( )( )-

( )( )̂, ̂ ̂ ( ) (

̂[( )( )— ( )( ) ̂, )

̂ √ ̂

̂ ̂ |⃗ ⃗|

̂ (ii) |⃗⃗ ( Q.16 √ Q.1 ̂ (d) √ ̂

√ ⃗⃗ | √

̂

√

√

̂ √ ) √ Find the area ( ) of a parallelogram, if its two sides are formed by the vectors ̂ ⃗⃗⃗ ̂ ̂ ̂ and ⃗⃗⃗ ̂ ̂ ̂ , ⃗⃗⃗ ̂, ⃗⃗⃗ Hint:̂ ̂ ̂ ̂ ̂) ( ̂ ̂) ⃗ ( ̂ ̂ ̂ ̂ ̂ ̂ ⃗ | |

(4)

Page 18 of 111 “Truth Is Ever To Be Found In The Simplicity, And Not In The Multiplicity And Confusion Of Things.” Newton

SCALARS &VECTORS CHAPTER # 2 ⃗ ⃗ ⃗ ⃗ | | |⃗⃗ Q.17 (√ Q.1 ) (d)

GOVT DEGREE COLLEGE S.R.E MAJEED, STADIUM ROAD NUMERICALS ̂| ̂,( ̂, ̂ √( √ √ ) ⃗| ⃗| ⃗⃗ | )( | ̂| | ̂| | )— ( )( ) ̂ [( )( )— ( )( )-

) ( )( )̂[( )( - ̂, ̂, ̂ ̂ ( ) ( )

2003 P/E Two forces of equal magnitudes are acting at a point; find the angle ( ) between the forces when the magnitude of resultant is also equal to the magnitude of either of these forces. (4) Hint:- Same as Q.2 (i) 2009 ( ) 2003 P/M ⃗ |) are acting at a point. The magnitude of their Two forces of magnitudes 10 N (| |) and 15 N (| ⃗ |). Find the angle ( resultant is 20 N (| ) between them. (4) Hint:- Same as Q.2 ( ) Find the angle ( ) between ⃗⃗⃗ Hint:- Same as Q.1 ̂ and ⃗⃗⃗ ̂ ̂ ̂. ̂ 2004 (4)

Q.18

Q.1

(d)

Q.19

Q.1

(d)

ARI F RAZA

̂

Q.20

Q.1

(d)

( ) Determine a unit vector perpendicular ( ̂ ⃗⃗⃗ ̂ ̂ ̂ ̂ ⃗⃗⃗ = ̂ ̂ Hint:- Same as Q.12 ̂ √ ̂ √ ̂ , ⃗⃗⃗ ̂ ⃗ ⃗ ̂ √ ̂

) to plane containing ⃗⃗ and ⃗⃗ if;

2005

(4)

Q.21

( √ Q.1

̂

√ (d)

̂

If ⃗⃗⃗ ̂ Prove that ⃗⃗⃗ Hint:-

√

̂) ̂ ⃗⃗⃗ ̂ ̂ (4) (⃗⃗⃗⃗ ̂ ⃗⃗⃗⃗ ̂ ⃗⃗⃗⃗ ̂ ) (⃗⃗⃗⃗ ̂ ⃗⃗⃗⃗ ̂ ⃗⃗⃗⃗ ̂ ) ( ) ( ) ( ̂) ( ̂) ( ̂ ) ( ̂ ̂ ̂ ̂ ̂ ̂ ̂ ̂ ̂

̂) ̂ ̂ ̂ ̂ ̂ 1994

Q.22

Q.1

(d)

Two vectors ⃗⃗ and ⃗⃗ are such that |⃗⃗ | , |⃗⃗ | and = 4 and ⃗⃗⃗ ⃗⃗⃗ ; Find:(i) The angle ( ) between ⃗⃗⃗ & ⃗⃗⃗ (ii) The magnitude | ⃗| Hint:- | | , |⃗ | , ⃗⃗⃗ ⃗⃗⃗ , (i) (ii) | ⃗ ⃗| (i) | || ⃗ | || ⃗ |

⃗|

(4)

Page 19 of 111 “Truth Is Ever To Be Found In The Simplicity, And Not In The Multiplicity And Confusion Of Things.” Newton

SCALARS &VECTORS CHAPTER # 2

GOVT DEGREE COLLEGE S.R.E MAJEED, STADIUM ROAD NUMERICALS

( )( ) ( ( | | | | | |⃗⃗ Q.23 ( Q.2 , ) (v) ⃗| ⃗| ⃗| ⃗| ⃗| ⃗⃗ | ̂ ̂ ̂ and ⃗⃗⃗ ̂ ̂ 2008 ̂ becomes (4) √| | √| | √( ) √ √ ) ) |⃗ | |⃗ | ( ) ( ) | || ⃗ | ⃗ ⃗ | || ⃗ |

(ii)

For what value of “p” are the two vectors ⃗⃗⃗ perpendicular to each other? Hint:- Same as Q.7
ARI F RAZA

Q.24

( Q.2

) (viii)

2009 If one of the Rectangular components of a force of 50 N (| |) is 25 N (|⃗⃗⃗ |); find the value of the other (|⃗⃗⃗ | ). (4) Hint:- Same as Q.11 |⃗⃗⃗⃗ | Determine a unit vector ( ̂ ̂ and ⃗⃗⃗ ⃗⃗⃗ ̂ ̂ Hint:- Same as Q.12 ̂ √ ̂ ̂ √ ̂ √ ) perpendicular to plane of ⃗⃗ and ⃗⃗ if; ̂ ̂ ̂ ̂ 2010 (4)

Q.25

( Q.2

) (vi)

Q.26

( √ Q.2

̂ (iii)

√

̂) √ Two vectors ⃗⃗ and ⃗⃗ are such that |⃗⃗ | ⃗| Find; | Hint:- |⃗⃗ | |⃗⃗ | |⃗⃗ ⃗⃗ | , | | ⃗| ⃗| √( ) ( ) .√ ⃗ ⃗ ⃗ ⃗ √| | √| | ( ) ⃗/ |⃗ | |⃗ | ⃗

, |⃗⃗ | (i) |

and |⃗⃗ ⃗|

⃗⃗ |

. (4)

,| || ⃗ | ⃗

⃗

| || ⃗ |

Page 20 of 111 “Truth Is Ever To Be Found In The Simplicity, And Not In The Multiplicity And Confusion Of Things.” Newton

SCALARS &VECTORS CHAPTER # 2

GOVT DEGREE COLLEGE S.R.E MAJEED, STADIUM ROAD NUMERICALS ⃗ | | | | ⃗| ⃗| ⃗| ⃗| √| | √( ) √ √ |⃗ | ( ) ( ⃗ )

(√

)

ARI F RAZA

Page 21 of 111 “Truth Is Ever To Be Found In The Simplicity, And Not In The Multiplicity And Confusion Of Things.” Newton

MOTION CHAPTER # 3

GOVT DEGREE COLLEGE S.R.E MAJEED STADIUM ROAD KARACHI. QUESTIONS

QUESTIONS

1992
Q.1 Q.2 Q.2 (a) (b) (a) Define Momentum and give its units in S.I. The Momentum of a moving body is its quantity of motion. Comment. (1+1+3) State and prove the law of conservation of Momentum. (1+4)

1993
Two masses are attached to the ends of a string which passes over a frictionless pulley such that they move vertically. Suppose , find the acceleration of the system and tension in the string. (4+4)

1994
Q.2 Q.2 (a) (b) Explain Displacement, Velocity and Acceleration, showing the difference between a uniform and nonuniform velocity and acceleration by graphic method. (5) Write down the equation of uniformly accelerated rectilinear motion. What is the most common example of uniformly accelerated motion? What is Free Fall Motion? (3+1+1) OR Explain Momentum and law of conservation of Momentum. (2+3) Define elastic collision in one dimension. (1) Two bodies having different masses and moving with different velocities have an elastic collision in one dimension. Calculate their final velocities after their collision. (3+3) What will happen if? (i) The masses of the two bodies are equal; (ii) The masses of the two bodies are equal and one of them is initially at rest. (1.5+1.5) Fill in blanks:(1) (ii) The product of mass and velocity is called Momentum. Write down whether the following statements are True or false:(2) (i) The motion of an air force solider descending with a parachute is a free fall motion. (F) (v) An inelastic collision is one in which the K.E and Momentum are conserved. (F) Select the correct answer for each from brackets:(1) (ii) A body remains at rest or continues to move with uniform velocity unless it is acted upon by ___. * A force * An un-balanced force *A force equal to the weight of the body * None of these
ARI F RAZA

Q.2 Q.2 Q.2

(a) (b) (c)

Q.8 Q.8

(a) (b)

Q.8

(c)

1995
Q.8 (b) Write down whether the following statements are True or false:(xii) The objects falling freely to the Earth move in the same direction. (1) (T)

1996
Q.2 (a) (i) Fill in the blanks:(2)  Whenever the average and instantaneous velocities of a body are equal, the body is said to have uniform velocity.  The dimensions of acceleration are (ii) Choose the correct answer for each from the given options:(1)  A rain drop continues to fall with a uniform velocity when ___. * Its weight is balanced by air friction * Its weight is balanced by air friction and up thrust * Its weight is balanced by air-up thrust Two bodies of equal masses are attached to two ends of a string which passes over a friction pulley. If Page 22 of 111 “Minds Are Like Parachutes: They Only Function When They're Open .” Thomas Dewar

Q.2

(b)

MOTION CHAPTER # 3

GOVT DEGREE COLLEGE S.R.E MAJEED STADIUM ROAD KARACHI. QUESTIONS the bodies are moving vertically, find:(i) Expression for tension in the string; (ii) Acceleration of the system.

(4+4)

1997
Q.2 (a) Write True or False:(2) (i) Elastic collision has conservation of energy but does not have conservation of Momentum. (F) (ii) In-elastic collision has conservation of Momentum but no conservation of kinetic energy. (T) Define the following term:(1) (i) Linear Momentum; State and prove the law of conversation of linear Momentum. (1+4)

Q.2

(b)

1998
Q.2 (a) (i) (ii) The S.I unit of Momentum is (Fill in the blank) (1) In an elastic collision the energy remains conserved whereas the Momentum does not. (Write True or False) (F) (1) (iii) Choose the correct answer from the given options:(1)  As a result of constant un-balanced force a body moves with ___. * Uniform velocity * Uniform acceleration * Variable speed * Uniform speed Two bodies of unequal masses attached to the ends of a string which passes over a frictionless pulley such that the two bodies move vertically. Find:(i) Acceleration of the system; (ii) Tension in the string. (3+3) (i) When a body is placed on an inclined frictionless plane, the force by which the body slides is equal to or (Fill in the blank) (1)
ARI F RAZA

Q.2

(b)

Q.3

(a)

1999
Q.1 Q.2 (a) (a) Fill in blank with the correct answer:(i) The product of mass & velocity is called Momentum. State True or False for the following statements:(i) In an elastic collision kinetic energy is conserved but not the Momentum. (ii) In an in-elastic collision Momentum is conserved but not the kinetic energy. Define the following term:(i) Linear Momentum; State and prove the law of conservation of linear Momentum (1) (2) (F) (T) (1) (1+4)

Q.2

(b)

2000
Q.2 (a) Fill in the blanks:(2) (i) A body remains at rest or continues to move with uniform velocity unless acted upon by unbalanced force. (ii) Frictional force is a self-adjusting force and it is said to be maximum when the body starts sliding. (i) Two spherical bodies of different masses moving with different velocities along same line collide elastically with one another. Find expression for the final velocity of only one of the two bodies after collision? (6) (ii) Derive expression for the acceleration of a body of mass moving down a plane of inclination having friction . (3)

Q.2

(b)

2001
Q.2 (a) Choose the correct answer from the given options:(i) In an in-elastic collision ___. * Momentum is conserved but K.E. is not conserved “Minds Are Like Parachutes: They Only Function When They're Open .” Thomas Dewar (1) Page 23 of 111

MOTION CHAPTER # 3

GOVT DEGREE COLLEGE S.R.E MAJEED STADIUM ROAD KARACHI. QUESTIONS * K.E is conserved but Momentum is not conserved * Both Momentum & K.E are conserved * Neither Momentum nor K.E is conserved Two masses are attached with the ends of a string which passes over a frictionless pulley such that mass is placed on a smooth horizontal plane surface and the mass moves vertically downwards. Find the acceleration of the system and tension in the string. (2+2) State and prove the law of conservation of linear Momentum. (1+3) Choose the correct answer from the given options:(1) (ii) The acceleration of a body moving down a smooth plane inclined at will be ___. * * * *

Q.2

(b)

Q.3 Q.4

(c) (a)

2002 P/E
Q.1 Q.2 (b) (a) Define linear Momentum. Explain the law of conservation of linear Momentum. (1+2) Choose the correct answer for each from the given options:(2) (i) Under the influence of a constant unbalanced force a body moves with a ___. * Uniform velocity * Uniform acceleration * Variable acceleration * Uniform speed (ii) According to Stokes’s law, the force exerted on a sphere of radius moving vertically down with constant velocity in a liquid of viscosity is given by ___. * * * * A block of mass is pulled up on a smooth inclined plane with a constant force . Obtain an expression for the acceleration of the block if the force of friction between the block and plane is . Choose the correct answer for each from the given options:(1) (iii) A helicopter of mass riese vertically with a constant speed of . What resultant force acts on the helicopter ? * * * *
ARI F RAZA

Q.2 Q.3

(b) (a)

2002 P/M
Q.1 (a) Choose the correct answer for each from the given options:(2) (ii) If the speed–time graph of a body is a straight line parallel to time-axis, its acceleration will be ___. * Zero * Maximum * Minimum * Uniform (iii) Stokes’s law holds good for the ___. * Bodies of all shapes * Motion through viscous medium * Motion through non-viscous medium * Motion through a vacuum Two spheres of different masses moving with different velocities along the same line makes elastic collision. Derive the expression for the velocity of one of the spheres after collision. (5) Choose the correct answer for each from the given options:(1) (i) A stone when falling from a height of , strikes the ground with velocity of ___. * * * * What is an inclined plane? Find expressions for the downward acceleration of a body on an inclined plane both in the presence and the absence of friction. (1+4)

Q.1 Q.2

(c) (a)

Q.3

(c)

2003 P/E
Q.1 (c) Q.2 Q.3 (c) (a) Two equal masses are suspended from the two ends of a string which passes over a frictionless pulley in such a way that both of them hang vertically. Drive the formula for acceleration produced in both bodies. (4) A body is placed on an inclined plane. Find out the expressions for its downward acceleration both in the presence and absence of friction. (5) Choose the correct answer for each from the given options:(1) (ii) The unit of linear Momentum is ___. * * * * Choose the correct answer for each from the given options:(2) Page 24 of 111 “Minds Are Like Parachutes: They Only Function When They're Open .” Thomas Dewar

Q.4

(a)

MOTION CHAPTER # 3 (i)

GOVT DEGREE COLLEGE S.R.E MAJEED STADIUM ROAD KARACHI. QUESTIONS In an inelastic collision ___. * Both Momentum & K.E are conserved * Neither Momentum nor K.E is conserved * Only Momentum is conserved * Only kinetic energy is conserved When a body slides over a surface, the kinetic friction ( ___. * * *

(iii)

) and static friction ( ) are related as *

2003 P/M
Q.1 Q.2 (b) (a) Give the definition of force on the basis of Newton’s first law of motion. Starting with prove that force is also given by the rate of change of Momentum. (1+2) Select the correct answer for each from the given options:(1) (i) A car is traveling at north, turns west without a change in speed. The car is moving with ___. * Uniform velocity * Acceleration * Average velocity * None of them (ii) How much height does a free falling body of mass lose in ? * * * * Two bodies of unequal masses connected to the two ends of a string, which passes over a frictionless pulley, move vertically. Derive an expression to show that acceleration in the bodies is half of acceleration due to gravity if (5) Select the correct answer for each from the given options:(1) (iii) A body goes from to mark and back to mark in . Its average speed is ___. * * * * State and prove the law of conservation of linear Momentum. (1+2)
ARI F RAZA

Q.2

(c)

Q.3

(a)

Q.4 Q.2

(b) (a)

2004
Select the correct answer for each from the given options:(2) (i) The rate of change of linear Momentum is equal to ___. * Acceleration * Force * Torque (iii) The acceleration of a body moving down a frictionless plane inclined at will be __. * * * Prove that all bodies slides with the same acceleration on a frictionless inclined plane. (4) Select the correct answer for each from the given options:(1) (iii) The unit of linear Momentum is ___. * * * * Give the difference between elastic collision and inelastic collision. Two spheres of unequal masses and moving with the initial velocities in the same direction collide elastically. Derive the relation of final velocity of body . (4)

Q.2 Q.3

(c) (a)

Q.3

(b)

2005
Q.2 (a) Select the correct answer for each from the given options:(2) (i) If the speed-time graph of a moving body is a curve, the body moves with ___. * Constant speed * Constant acceleration * Constant velocity * Changing acceleration (ii) In Stokes’s law, the viscous force is not proportional to ___. * Coefficient of viscosity * Radius of sphere * Terminal velocity * Mass of sphere Two unequal masses are connected to the two ends of a string which passes over a frictionless pulley such that both of them hang vertically. Derive expressions for their acceleration and tension in the string. (5) State and prove the law of conservation of linear Momentum. (1+3)

Q.2

(b)

Q.3

(b)

2006
Page 25 of 111 “Minds Are Like Parachutes: They Only Function When They're Open .” Thomas Dewar

MOTION CHAPTER # 3 Q.1 Q.2 (c) (a)

GOVT DEGREE COLLEGE S.R.E MAJEED STADIUM ROAD KARACHI. QUESTIONS Derive an expression for the acceleration of a body of mass moving down a plane of inclination having friction . (4) Select the correct answer for each from the given options:(2) (i) Equation represents ___. * Hooke’s law * Stokes’s law * Bragg’s law * Newton’s law (iii) How much height does a free falling body of mass lose in ? * * * * Two non-rotating spheres of unequal masses moving with the initial velocities in the same direction collides elastically. Derive the relation of final velocity of body . Select the correct answer for each from the given options:(1) (ii) The rate of change of linear Momentum is equal to ___. * Acceleration * Torque * Angular velocity * Force

Q.2 Q.3

(b) (a)

2007
Q.1 (a) Select the correct answer for each from the given options:(1) (iii) When a constant force is applied on a body, it moves with a ___. * Constant speed * Constant velocity * Constant acceleration * None Two bodies of unequal masses attached to the two ends of a string which passes over a frictionless pulley such that the two bodies hang vertically. Derive the expression for the acceleration of the bodies. (4) Select the correct answer for each from the given options:(1) (ii) Stokes’s law for fluid friction is given as ___. * * * * State and prove the law of conservation of linear Momentum. (1+3)
ARI F RAZA

Q.1

(c)

Q.4

(a)

Q.4 Q.1 Q.2 Q.4

(c) (d) (b) (a)

2008
Two non-rotating spheres of masses moving along a straight line with velocities respectively collide elastically. Derive an expression for the final velocity of mass . (4) Drive an expression for the acceleration of a body moving down an inclined plane where there is friction . (4) Select the correct answer for each from the given options:(1) (ii) In an in-elastic collision of two bodies ___. * K.E is conserved only * Momentum is conserved only * Both K.E & Momentum are conserved * Neither K.E nor Momentum is conserved

2009
Q.1 Choose the correct answer for each from the given options:(1) (iii) If a light object collides elastically with a massive body which is at rest, the light object will ___. * Rebound with the same velocity * Rebound with twice the velocity * Be stopped * Cause the massive body to move (ii) It is observed that all bodies sliding down a frictionless inclined plane have the same acceleration. How does this happen? Explain. (4) (a) Two bodies of unequal masses are attached to the ends of a string which passes over a frictionless pulley. If they are hung vertically, derive the expressions for the tension in the string and the acceleration of the bodies when the mass-string system is in motion. (7)

Q.2 Q.3

2010
Q.1 Choose the correct answer for each from the given options:(ii) Stokes’s law holds good for ___. * Bodies of all shapes * Motion through viscous medium * Motion through non-viscous medium * Motion through a vacuum (iii) How many meter(s) will a ball, starting from rest, fall freely in one second? “Minds Are Like Parachutes: They Only Function When They're Open .” Thomas Dewar (2)

Page 26 of 111

MOTION CHAPTER # 3

GOVT DEGREE COLLEGE S.R.E MAJEED STADIUM ROAD KARACHI. QUESTIONS * * * * It is observed that all bodies sliding down a frictionless inclined plane have the same acceleration. How does this happen? Explain. (4) Define Elastic Collision. Two spherical bodies of masses and moving with initial velocities and collide elastically in one dimension. Derive the expressions for their final velocities. (1+6)

Q.2 Q.3

(ii) (a)

2011
Q.1 Select the most appropriate answer for each from the given options:(i) The acceleration of a body moving down a frictionless plane inclined at * * * (xiii) Q.2 Q.4 (i) (a) (2) will be ___. * A stone, falling freely from a height of , strikes the ground with a velocity of ___. * * * * It is observed that all bodies sliding down a frictionless inclined plane have the same acceleration. How does this happen? Explain. (4) Two bodies of unequal masses are attached to the ends of a string which passes over a frictionless pulley. If one body moves vertically and the second body moves horizontally on a smooth horizontal surface, derive the expressions for tension in the string and the acceleration of the bodies. (7)

2012
Q.1 Select the most appropriate answer for each from the given options:(2) (ix) A helicopter weighing is moving up with a constant speed of . the force on the helicopter is ___. * * * * (xiv) The property of fluids due to which they resist their flow is called ___. * Static friction * Coefficient of friction * Viscosity * Terminal velocity (ix) In a translatory motion, it is not necessary for a body to move in a straight line. Discuss the statement. (4) (a) Define elastic and in-elastic collisions. Two non-rotating spheres of masses and , initially moving with the velocities and respectively in one dimension, collide elastically. Derive the expressions for their final velocities and . (1+6)
ARI F RAZA

Q.2 Q.3

Page 27 of 111 “Minds Are Like Parachutes: They Only Function When They're Open .” Thomas Dewar

MOTION

CHAPTER # 3

NUMERICALS NUMERICALS
Q.1 Q.2 (c) A ( ) gun ( projectile ( ( velocity of the gun ( ) mounted on wheels shoots a ( ) ) with a muzzle velocity of ( ) above the horizontal. Find the horizontal recoil (5)

) at an angle of ).

ARI F RAZA

Hint:-

, , ( ( ), ),

(

)( )

(

)( )

( )( ( )( ( )(

) ) )

(

)(

)

( Q.2 Q.2

) (c)

1992 A minibus starts moving from the position of rest ( ) at a bus stop with a uniform acceleration. During the 10th second of its motion it covers a distance of 95 m ( ). Calculate its acceleration ( ) and the total distance covered ( ) in 10 seconds. (5)

Page 28 of 111 “The Mediocre Teacher Tells. The Good Teacher Explains. The Superior Teacher Demonstrates. The Great Teacher Inspires.” William Arthur Ward

MOTION

CHAPTER # 3

Hint:(i) (ii) (i) ( )( ) ( ) ( ) ( )

( )( ) ( )

( )

ARI F RAZA

( )

(ii)

( ) ( )

Q.3

( Q.2

, (c)

) 1994 A boy throws a ball vertically upwards with a speed of 25 m/s ( ). On its way down it is caught at a point 5 m ( ) above the ground. How fast ( ) was it coming down at that point? How long did the trip take ( )? (4)

Hint:Page 29 of 111 “The Mediocre Teacher Tells. The Good Teacher Explains. The Superior Teacher Demonstrates. The Great Teacher Inspires.” William Arthur Ward

MOTION

CHAPTER # 3

(i) (ii) (i) ( ) ( ( )( ) )

,

√

√

(ii)

( (

) )
ARI F RAZA

√ ( √ √ ) √( ) ( )( )

Q.4

( Q.2

, (c)

) ) 1996 A wooden block ( ) of ( ) is hanging by a string on which a bullet of ( ) has been shot. If the bullet sticks with the block ( ) and is raised up to 5 cm ( ); find the velocity of the bullet ( )? (5) Hint:-

(

,

Page 30 of 111 “The Mediocre Teacher Tells. The Good Teacher Explains. The Superior Teacher Demonstrates. The Great Teacher Inspires.” William Arthur Ward

MOTION

CHAPTER # 3

ARI F RAZA

(

)( )

(

)(

)

(

)( )

(

)( )

( )

(

)

(

)

√ √ √ √ ( )

√

Q.5

( Q.2

) (c)

1997 Two bodies A and B are attached to the two ends of string which passes over a frictionless pulley such that the masses hang vertically. If the mass of the one body is ( ). Find:(i) The mass of the second body ( ) which moves downward with an acceleration of ( ); (ii) The tension ( ) in the string. (6) Hint:, , , (i) ( )

Page 31 of 111 “The Mediocre Teacher Tells. The Good Teacher Explains. The Superior Teacher Demonstrates. The Great Teacher Inspires.” William Arthur Ward

MOTION ( ( ) ) ( )

CHAPTER # 3

(ii) ( ( ( )( ) ) )

Q.6

( Q.2

, (c)

Q.7

(281.4 m/s) Q.2 (c)

) 1998 A 50 g ( ) bullet is fired in to 10 kg ( ) wooden block ( ) that is suspended by a long chord so that it can swing as pendulum. If the block is displaced ( ) so that its center of gravity rises by 10 cm ( ), what is the speed of the bullet ( )? (5) Hint:- Same as Q.4 1999 A motor car is moving up a slope of ( ) with a velocity of ( ). Suddenly the engine fails ( ). How much will the car move ( ) before coming to rest. Assume frictionless surface. (4) Hint:, , ,
ARI F RAZA

( ( ) (

(

)

) )

Q.8

( Q.2

) (d)

2000 Two blocks of masses ( ) and ( ) are attached to the ends of a string which passes over a frictionless pulley in such a way that block of mass lies on a horizontal surface and the other block hangs vertically. Find the acceleration ( ) of the system and tension ( ) in the string. (4) Hint:, , , (i) ( ( ( ) ) )

Page 32 of 111 “The Mediocre Teacher Tells. The Good Teacher Explains. The Superior Teacher Demonstrates. The Great Teacher Inspires.” William Arthur Ward

MOTION

CHAPTER # 3

(ii) ( ( ) )

Q.9

( Q.1

, (d)

) A machine gun fires ( ) per second ( ( ) and has a speed of ( ( ) necessary to hold the gun in position. Hint:, , ,

2001 ) in to a target. Each bullet weighs ). Find the force (4) , ,

( ( ( Q.2 ) (d)

) )
ARI F RAZA

Q.10

Q.11

( Q.4

(d)

2002 P/E A car starts from rest ( ) and moves with a constant acceleration. During the of its motion it covers a distance of ( ). Calculate:(i) The acceleration ( ) of the car; (ii) The total distance covered by car during this time ( ). (4) Hint:- Same as Q.2 ) ( ) bullet ( ) is fired from ( ) gun ( ) with a speed of ( ). What is the speed of the recoil of gun ( )? (4) Hint:, , , , ,

(

)( )

(

)( )

( (

)( )( )

)

( )( ) ( )( )

Q.12

( Q.3

) (d)

A ( ( Hint:-

(

2003P/M ) golf ball moving with a velocity of ( ), collides with an ) steel ball at rest ( ). If the collision is elastic, compute the velocities ) of both balls after the collision. (4) , , , , ,

Page 33 of 111 “The Mediocre Teacher Tells. The Good Teacher Explains. The Superior Teacher Demonstrates. The Great Teacher Inspires.” William Arthur Ward

MOTION (i) ( ( ( ( (ii) ( ( ( ) ) ) ( ( ) ) ) ) ) ) ( ( ) )

CHAPTER # 3

Q.13

( Q.4

, (d)

) 2004 A wooden ball of mass ( ) is suspended by a thread. The horizontal current of air blows it to one side such that the thread makes an angle of ( ) with vertical; find the tension ( ) in the thread and force of air current ( ). (4) Hint:, , ,
ARI F RAZA

( )

and

( )

Page 34 of 111 “The Mediocre Teacher Tells. The Good Teacher Explains. The Superior Teacher Demonstrates. The Great Teacher Inspires.” William Arthur Ward

MOTION

CHAPTER # 3

( )

( )

( )

Q.14

( Q.2

, (d)

) A ( ( Hint:,

Q.15

( Q.1 ( Q.4 ( Q.2

(d) ) (d) ) (d)

2005 ) golf ball moving with a velocity of ( ), collides with an ) steel ball at rest ( ). If the collision is elastic, compute the velocities ) of both balls after the collision. (4) Same as Q.12 ) 2006 A ball is thrown vertically upwards from the ground with a speed of ( ). On its way down it is caught at a point ( ) above the ground. How long did the trip take ( )? (4) Hint:- Same as Q.3 (
ARI F RAZA

Q.16

A ( ) bullet ( ) is fired from ( speed of ( ). What is the speed of the recoil of gun ( Hint:- Same as Q.11

) gun ( )?

) with a (4)

Q.17

2007 A boy throws a ball upward from the top of a tower with a speed of ( ). On the way down it just misses the thrower and falls to the ground ( ) below. Find how long ( ) the ball remains in air. (4) Hint:, , ,

( (

) )

Page 35 of 111 “The Mediocre Teacher Tells. The Good Teacher Explains. The Superior Teacher Demonstrates. The Great Teacher Inspires.” William Arthur Ward

MOTION

CHAPTER # 3

ARI F RAZA

√ ( √ √ ) √( ) ( )( )

( Q.18 ( Q.2 ) (ix)

)

2008 A helicopter weighs ( ). a) Calculate the force ( ) on it if it is ascending at a rate of ( ); b) What will be the force ( ) on the helicopter if it is moving vertically with the constant speed of )? (4) Hint:(a) (b) (a)

. /
Page 36 of 111 “The Mediocre Teacher Tells. The Good Teacher Explains. The Superior Teacher Demonstrates. The Great Teacher Inspires.” William Arthur Ward

MOTION . /

CHAPTER # 3

(b) ( )

Q.19

( Q.2

, (vii)

) 2010 A wooden block ( ) having ( ) mass is suspended by a long cord, that can swing as a pendulum. A ( ) bullet is fired which lodges itself in to the block ( ). Due to impact, the center of gravity of the block is raised by ( ). What was the initial speed of the bullet ( )? Hint:- Same as Q.4 2011

(

)

ARI F RAZA

Page 37 of 111 “The Mediocre Teacher Tells. The Good Teacher Explains. The Superior Teacher Demonstrates. The Great Teacher Inspires.” William Arthur Ward

Motion In Two Dimensions CHAPTER # 4

QUESTIONS

[e-mail]

QUESTIONS

1994
Q.8 (a) Fill in the blanks:(iii) At maximum height the vertical velocity of a projectile is (1) .

1995
Q.2 (a) A particle is projected at an angle to the horizontal with velocity and is allowed to fall freely so that it covers a certain distance in a parabolic path. Prove that the expressions for the total time of flight and the horizontal range are given by:(7)

Q.2

(b)

Q.8

(c)

In the game of cricket a ball of high trajectory is easy to catch. Explain it? (3) Ans:- In cricket, a ball with high trajectory is easy to catch since the time of flight is so long that the fielder has plenty of time to get in to position, whereas in the case of low trajectory it is much harder to catch the ball since the time of flight is not so long. Select the correct answer for each from the given options:(2) (xxii) When a particle moves in a circle, the angle between its linear velocity and angular velocity is always ___. * * * * (xxviii) The angular speed of the second hand of a watch is ___ rad/sec.
ARI F RAZA

*

*

*

1

*

None of these

1996
Q.3 (a) (i) Fill in blanks:(2) (a) One radian is equal to . (b) The time rate of change of angular velocity is called angular acceleration. (ii) Choose the correct answer from the given options:(2) (a) Every point on a rotating body has the same ___. * Linear velocity * Angular velocity * Angular Momentum * None of these (b) When a body is thrown vertically upwards, it is a case of ___. * Free fall motion * Projectile motion * Under-gravity motion A body is rotating with a uniform linear speed in a circular path of radius . Derive a formula for its Centripetal acceleration. (7)

Q.3

(b)

1997
Q.4 Write short notes on:(i) Centripetal force. “If One Can Not See Gravitation Acting Here, He Has No Soul.” Richard P. Feynman (7.5) Page 38 of 111

Motion In Two Dimensions CHAPTER # 4

QUESTIONS

[e-mail]

1998
Q.3 (a) Write down whether the following statement is True or False:(1) There is no difference between rotatory motion and circular motion. (T) (iii) Choose the correct answer from the given options:(1) The range of Ghori missile is ___ km. * * * * (b) Define projectile motion. A shell is shot from a gun at an angle with the horizontal with an initial velocity . Derive the expression:(i) For the Maximum Height of projectile; (ii) For the Range of the projectile. (7) Write note on any two of following:(7.5) (i) Centripetal force. (ii)

Q.3

Q.4

2000
Q.3 (a) Choose the correct answer for each from the given options:(4) (i) Maximum height of the projectile depends upon ___. * Angle of projection * Velocity of projection * Both angle & velocity * None of these (ii) S.I. unit of angular velocity is ___. * m.sec * rad/sec * deg/sec * rev/sec (iii) When a body moves along the circumference of a circle with uniform speed, changes takes place in its ________. * Linear velocity * Tangential acceleration * Both (iv) When a body moves along a parabolic path, which component of its velocity does not change? * Horizontal * Vertical (i) Describe projectile motion, explaining the changes in vertical and horizontal components of the velocity. (2) (ii) Derive expressions for Maximum Height and Range of a projectile. (4) Why there are two possible angles of projection for the same range with the same velocity of projection? (1)
ARI F RAZA

Q.3

(b)

( ( , ( (i) ( ) ), ( , ( √ (ii) ( ) √ )( ) )), ( )-

) ) ), ( , ( )( ) )-

(

)

, ( , (

, ( ( )

, ( )-

)-

(iii) ( )

, ( , (

))-

, ( , ( )( )

)-

( )( )

( )

(

)

(

) Page 39 of 111

“If One Can Not See Gravitation Acting Here, He Has No Soul.” Richard P. Feynman

Motion In Two Dimensions CHAPTER # 4

QUESTIONS

[e-mail]

2001
Q.3 (a) Choose the correct answer for each from the given options:(i) One radian is equal to ___. * * * * (ii) Every point on a rotating rigid body has the same ___. * Linear velocity * Linear Momentum * Angular velocity * Linear acceleration (iii) The angle between centripetal acceleration and tangential acceleration is ___. * * * * Define Centripetal Force. Prove that Centripetal Acceleration is (3)

Q.3

(b)

2002P/E
Q.2 (a) Choose the correct answer for each from the given options:(iii) The centripetal acceleration of a body moving along a circle is ___. * Q.2 Q.4 (c) (a) * * * (1)

Define projectile motion. A projectile is thrown in air at an angle with the ground level with the velocity . Establish the equations for the Total time of flight and Range of the projectile. (1+2+2) Choose the correct answer for each from the given options:(1) (i) A body is moving along a circle with an increasing speed. It possesses ___. * Tangential acceleration only ( ) * Centripetal acceleration only ( ) * ( )
ARI F RAZA

* Q.4 (a)

No acceleration

2002P/M
Select the correct answer for each from the given options:(3) (i) If a projectile is launched at with velocity , it hits a target. It will have double range if its velocity is ___. * * * *

√ √ √ (√ (ii)

( ) ( ) )

(iii)

√ If “r” is the radius of the circular path of a particle, its linear and angular velocities are related as ___. ⃗ ⃗ ⃗ ⃗ * ⃗ * ⃗ * ⃗ * ⃗ If a projectile is thrown at an angle of , it hits a target. It will have the same range if it is thrown at an angle of ___.   

Q.4

(c)

A shell is fired upward at angle an angle “θ” with the horizontal with the speed “Vo”. Find:Page 40 of 111 “If One Can Not See Gravitation Acting Here, He Has No Soul.” Richard P. Feynman

Motion In Two Dimensions CHAPTER # 4 (i) (ii) Q.3 (a) Time to reach maximum height; Horizontal range.

QUESTIONS

[e-mail]

2003 P/E
Choose the correct answer:(iii) In projectile motion a body moves with ___.  Constant vertical component of velocity  Constant horizontal component of velocity  Both changing horizontal and vertical components of velocity  Horizontal component changing but vertical component of velocity constant Derive an expression for the centripetal acceleration produced in a body. Choose the correct answer:(ii) Due to presence of air resistance, the total time of flight of a projectile ___.  Remains same  Decreases  Increases  Becomes zero (iii) A projectile is fired with the initial velocity of 90 m/s to hit a ground level target. It’s maximum horizontal range will be ___.  9.2 m  826.5 m  413 m  81 m
ARI F RAZA

Q.3 Q.4

(c) (a)

2004
Q.2 (a) Choose the correct answer:(i) The motion on a curved path, when one component of velocity is constant and other is variable is called ___.  Circular motion  Projectile motion  Vibratory motion  None of these An object is thrown in air at an angle “θ” with the horizontal with velocity “Vo”. Derive the relation for:(i) The total time of flight; (ii) The horizontal range of the projectile Choose the correct answer:(i) If “ω” is the angular speed of a particle moving in a circle of radius “r”, the centripetal acceleration will be ___.  ωr 2  ωr 2  ωr  None of these (ii) Every point on the rotating body has the same ___.  Linear velocity  Angular velocity  Linear acceleration  None of these

Q.2

(b)

Q.4

(a)

2005
Q.2 (a) Choose the correct answer:(iii) When a body moves with a constant speed in a circle ___.  Its velocity is changing  Its acceleration is zero  Its acceleration is increasing Page 41 of 111 “If One Can Not See Gravitation Acting Here, He Has No Soul.” Richard P. Feynman

Motion In Two Dimensions CHAPTER # 4

QUESTIONS

[e-mail]

Q.3

(a)

Q.4

(c)

 Its velocity is uniform Choose the correct answer:(i) The angle between centripetal acceleration and tangential acceleration is ___.  00  900  1800  450 Derive an expression for the centripetal acceleration of a mass “m” moving in a circle of radius “r” with the speed “V”

2006
Q.3 Q.4 (b) (a) Define projectile motion. A shell is fired with the velocity “Vo” at angle “θ” with the ground to hit the ground level target. Find out the expressions for the total time of flight and horizontal range. Choose the correct answer:(i) One radian is equal to ___.  0.0170  57.30  35.70  0.170 (ii) If “r” is the radius of the circular path of a particle its linear acceleration ( ⃗ ) and angular acceleration ⃗ are related by ___.  ⃗ ⃗ ⃗    Derive the expressions for centripetal acceleration and centripetal force.
ARI F RAZA

Q.4 Q.2

(b) (a)

2007
Choose the correct answer:(i) Centripetal force is called ___.  Centrifugal force  Center-seeking force  Tangential force  None of these Define and derive the expression for centripetal acceleration. What is a projectile? Derive the following expressions for a projectile:(i) Maximum height; (ii) Horizontal range.

Q.2 Q.4

(a) (b)

2008
Q.2 (a) Choose the correct answer:(ii) An angle subtended at its center by an arc whose length is equal to its radius is ___.  37.30  47.30  57.30  67.30 Choose the correct answer:0 0 (i) Two projectiles A & B are thrown up with the same speed at an angle of 60 & 30 respectively with the horizontal, then ___.  The range of A will be greater  The range of B will be greater  The range of A & B will be same  The range is independent of angles (ii) Which of following is a spin motion? Page 42 of 111 “If One Can Not See Gravitation Acting Here, He Has No Soul.” Richard P. Feynman

Q.3

(a)

Motion In Two Dimensions CHAPTER # 4

QUESTIONS

[e-mail]

Q.3

(b)

Q.4

(a)

 The motion of the planets round the Sun  The motion of electrons round the nucleus  The motion of Moon round the Earth  The daily rotation of Earth causing day & night Define angular velocity & angular acceleration. Show that:(i) V = rω; (ii) a = r ; where the symbols have their usual meanings. Choose the correct answer:(iii) A body moves along a circular path with an increasing speed possesses ___.  Tangential acceleration only  Centripetal acceleration only  Both tangential and centripetal only  No acceleration

2009
Q.1 Choose the correct answer for each from the given options:0 (ix) A projectile is thrown at an angle of 30 with the horizontal having a certain velocity. It will have the same range if thrown with the same velocity as before at an angle of ___.  450  600  750  150
ARI F RAZA

2010
Q.1 Choose the correct answer for each from the given options:(iv) The horizontal range of a projectile depends upon ___.  The angle of projection  The velocity of the projectile  “g” at the place  All of them (xi) A cyclist cycling around a circular racing track skids because ___.  The centripetal force upon him is less than the limiting friction  The centripetal force upon him is greater than the limiting friction  The centripetal force upon him is equal than the limiting friction  None of these (v) At what points will the speed of a projectile be maximum? Calculate the range of the projectile? (b) Define centripetal acceleration and derive its formula.

Q.2 Q.5 Q.1

2011
Select the most appropriate answer for each from the given options:(xiv) When the angular velocity of a disk increases, angular acceleration and angular velocity are ___.  Parallel  Non-parallel  Perpendicular  None of these (i) In the game of cricket, why is it easy to catch a ball of high trajectory? In volley ball, cricket, a ball with high trajectory is easy to catch since the time of flight is so long that the fielder has plenty of time to get in to position, whereas in the case of low trajectory it is much harder to catch the ball since the time of flight is not so long. (a) What is projectile motion? A shell is fired with a velocity at an angle with the horizontal to target at the ground level. Derive the expressions for: (i) Total time of flight; (ii) Horizontal range.

Q.2 Ans.

Q.3

Page 43 of 111 “If One Can Not See Gravitation Acting Here, He Has No Soul.” Richard P. Feynman

Motion In Two Dimensions CHAPTER # 4

NUMERICALS

shahali_81@.com

NUMERICALS
Q.1 A mortar shell is fired at a ground level target 490 m ( ) away with an initial velocity of 98 m/s ( ). Find the two possible values of launch angle ( ). Calculate the minimum time ( ) to hit the target. Hint:( ) ( ) (15 & 75 , 5.176 sec) 1995 A string 1 m ( ) long would break when its tension is 69.6 N ( ). Find the greatest speed ( ) at which a ball of mass 2 kg ( ) can be whirled with the string in a vertical circle. Hint:√ √ (5.9 m/s) 1996 0 An artillery cannon is pointed upward at an angle 35 ( ) with respect to the horizontal and fires a projectile with an initial velocity of 200 m/s ( ). If the air resistance is negligible, find:(i) The maximum height ( ) of the projectile; ( ) ( ( ) ( ) ) Hint:(ii) Range ( ) of the projectile. ( ) ( ) Hint:(671.22 m, 3835.10 m) 1998 A bullet was fired horizontally with 20 m/s ( ) from the top of a building 20 m ( ) high. When the bullet was 10 m ( ) above the ground, accidentally it hits a bird. Find the time taken ( ) by the bullet to hit the bird and the velocity ( ) of bullet when it hits bird. Hint:ARI F RAZA

0

0

Q.2

Q.3

Q.4

(a)
( ( ) √ √ )

(b)
( √( ) ( ) )( √( ) ) ( ) √ √

Q.5

Q.6

(1.428 sec, 24.41 m/s) 2000 A ball of mass 0.2 kg ( ) is tied to the end of a circle and whirled in a horizontal circle of radius 0.4 m ( ). If the ball makes 10 complete revolutions ( ) in 4 sec ( ), find the linear speed ( ), centripetal acceleration ( ) and centripetal force ( ). Hint:- (a) (b) (c) 2 (6.28 m/sec, 98.57 m/s , 19.71 N) 2001 0 A machine gun is pointed upward at an angle of 30 ( ) with respect to the horizontal and fires a projectile with a velocity of 200 m/s ( ). Find:(i) Maximum height ( ) of the projectile; Hint:- Same as Q.3 (i) (ii) Range of the projectile ( ). Hint:- Same as Q.3 (ii) (510.20 m, 3534.79 m) 2002P/E

Page 44 of 111 “If Quantum Mechanics Hasn't Profoundly Shocked You, You Haven't Understood It Yet.” Niels Bohr

Motion In Two Dimensions CHAPTER # 4 Q.7

NUMERICALS

shahali_81@.com

A player thrown ball at an initial velocity of 36 m/s ( ). Calculate the maximum distance ( ) reached by ball, assuming the ball is caught at the same height at which it was released. If he wishes to throw the ball half the maximum distance( ) in the shortest possible time, compute the angle of elevation ( ).

Hint:- (a) Hint:- (b)
0

(

)

(

)

(

)

Q.8

(132.24 m, 15 ) 2002 0 Two possible angles to hit a target by a mortar shell fired with an initial velocity of 98 m/s ( ) are 15 ( ) and 0 75 ( ) respectively. Calculate the range ( ) of the projectile and the minimum time ( ) required to hit the target. ( ) ( ) Hint:- (a)
ARI F RAZA

(b) Q.9 (490 m, 5.176 sec) 2004 0 What is the take-off speed ( ) of a locust if its launching angle is 55 ( ) and its range is 0.8 m ( )? Hint:√ √ ( ) (2.88 m/s) 2005 0 A machine gun is pointed upward at an angle of 30 ( ) with respect to the horizontal and fires a projectile with a velocity of 200 m/s ( ). Find:(iii) Maximum height ( ) of the projectile; Hint:- Same as Q.3 (i) (iv) Range of the projectile ( ). Hint:- Same as Q.3 (ii) (510.20 m, 3534.79 m) 2006 Calculate centripetal acceleration ( ) and centripetal force ( ) on a man whose mass is 80 kg ( ) and who is resting on the ground at the equator, given that the radius of Earth is 6.4x106 m ( ) and the Earth completes one rotation in one day ( ). Hint:- (a)
( )

Q.10

Q.11

(b) 2 (0.0338 m/s , 2.70 N)

Q.12

2006 Calculate centripetal acceleration acting on a man whose mass is 64 kg when he is resting on the ground at the equator. (Re = 6.4x106 m) Page 45 of 111 “If Quantum Mechanics Hasn't Profoundly Shocked You, You Haven't Understood It Yet.” Niels Bohr

Motion In Two Dimensions CHAPTER # 4

NUMERICALS

shahali_81@.com

Q.13

Q.14

Hint:- Same as Q.11 2 (0.0338 m/s ) 2007 A rocket is fired at a ground level target 600 m ( ) away with an initial velocity of 85 m/s ( ), find the two possible values of the launch angle ( ). Calculate the minimum time ( ) to hit the target. 0 0 (27.28 , 62.72 & 7.95 sec) Hint:- Same as Q.1 2008 A mortar shell is fired at a target 800 m ( ) away with the velocity of 100 m/s ( ). Calculate the maximum possible value of the launch angle ( ). ( ) Hint:( ) (64.19 ) 2009 Calculate centripetal acceleration ( ) and centripetal force ( ) on a man whose mass is 80 kg ( ) and when resting on the ground at the equator. The radius of Earth is 6.4x106 m ( ). Hint:- Same as Q.11 2 (0.0338 m/s , 2.70 N) 2011
0

Q.15

ARI F RAZA

Page 46 of 111 “If Quantum Mechanics Hasn't Profoundly Shocked You, You Haven't Understood It Yet.” Niels Bohr

TORQUE, ANGULAR MOMENTUM & EQUILIBRIUM CHAPTER # 5

QUESTIONS

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QUESTIONS

1992
Q.3 (a) Which of following statement is the most appropriate? (i) The direction of torque is the same as the direction of the corresponding applied force (ii) The direction of the torque is opposite to the direction of applied force (iii) The direction of the torque is perpendicular to the direction of applied force Define equilibrium? and state its two conditions.

Q.3 Q.

(b)

1994
Fill in the blanks:(iv) The physical quantity which tends to rotate a body is called torque.

1995
Q. Fill in the blanks:(vi) The imaginary line about which a body rotates is called axis of rotation. (vii) The torque acting on a particle is the time rate of change of its angular Momentum. (ix) A body is said to be in equilibrium if the net force on it is zero. Choose the correct answer:(xxiii) The physical quantity which produces angular acceleration is called ___.  Centripetal force  Centrifugal force  Torque  None of these
ARI F RAZA

Q.

1996
Q.4 Q.4 Q.2 (a) (b) (b) Fill in the blanks:(i) For the translation equilibrium the net force acting on the body must be equal to zero. Define equilibrium and its different conditions.

1997
Q.4 Define the following terms:(ii) Angular Momentum; (iii) Torque. Write short notes on:(iii) Conditions of equilibrium.

1998
Q.4 Write short notes on any two of the following:(ii) Conditions of equilibrium; (v) Center of mass.

1999
Q.2 (b) Q.4 Define the following terms:(ii) Angular Momentum; (iii) Torque. Write short notes of any two of the following:(i) Conditions of equilibrium; (iv) Law of conservation of angular Momentum.

2000
Q.4 (a) True and false:Page 47 of 111 “Science Cannot Solve The Ultimate Mystery Of Nature. And That Is Because, In The Last Analysis, We Ourselves Are A Part Of The Mystery That We Are Trying To Solve.” Max Planck

TORQUE, ANGULAR MOMENTUM & EQUILIBRIUM CHAPTER # 5 (ii) (i) (ii)

QUESTIONS

[e-mail] (F)

Q.4 Q.4 Q.4

(b) (b) (c)

Center of gravity of an object always coincides with its center of mass. What is couple? Find moment of couple? State and explain the conditions of equilibrium

2001
Define the terms:(i) Torque; (ii) Moment of couple; (iii) Angular Momentum.

2002P/E
Q.3 (a) Choose the correct answer:(ii) The rate of change of angular Momentum is equal to ___.  Force exerted on the body  Torque  Force exerted by the body  Angular acceleration Define torque and explain it. Give its units. State and explain law of conservation of angular Momentum of a particle.

Q.3 Q.4 Q.1 Q.2

(c) (c) (b) (a)

2002P/M
Define an expression for the torque acting on the body.
ARI F RAZA

2003P/E
Choose the correct answer:(iii) The physical quantity which produces angular acceleration is called ___.  Torque  Work  Power  Energy Define the following:(i) Center of mass; (ii) Torque; (iii) Angular Momentum. Choose the correct answer:(ii) Two forces which are equal in magnitude but opposite in direction and are not acting along the same line constitute a ___.  Couple  Circle  Power  Force Define moment of a couple and derive an expression for it.

Q.2

(b)

Q.4

(a)

Q.4 Q.3

(c) (a)

2003P/M
Choose the correct answer:(ii) The unit of angular Momentum is ___.  N.s  J.s  N.m  None of these

2004
Q.3 (a) Choose the correct answer:(ii) When the net torque acting on the system is zero, which of the following will be constant? Page 48 of 111 “Science Cannot Solve The Ultimate Mystery Of Nature. And That Is Because, In The Last Analysis, We Ourselves Are A Part Of The Mystery That We Are Trying To Solve.” Max Planck

TORQUE, ANGULAR MOMENTUM & EQUILIBRIUM CHAPTER # 5     Q.4 (a) Force Angular Momentum Liner Momentum None of these

QUESTIONS

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2005
Choose the correct answer:(ii) The rate of change of angular Momentum is also called ___.  Force  Acceleration  Inertia  Torque Define equilibrium. State the conditions of equilibrium.

Q.4 Q.1

(b) (a)

2006
Choose the correct answer:(ii) The S.I. unit of angular Momentum is ___.  kg.m/s  kg.m.s  J.s  J/s Choose the correct answer:(iii) Two forces which are equal in magnitude but opposite in direction constitute a ___.  Couple  Circle  Power  Force State and explain the first condition of equilibrium.
ARI F RAZA

Q.4

(a)

Q.4 Q.2

(c) (a)

2007
Choose the correct answer:(ii) The rate of change of angular Momentum with respect to time is ___.  Force  Angular velocity  Torque  Angular acceleration Define the following:(i) Static equilibrium; (ii) Dynamic equilibrium; (iii) Couple; (iv) Angular Momentum.

Q.2

(c)

2008
Q.2 (a) Choose the correct answer:(iii) The center of a mass of a system of particles ___.  Always coincide with the center of gravity  Never coincide with center of gravity  Coincides with the center of gravity in a uniform gravitation field  Coincides with the center of gravity in a non-uniform gravitational field Define a couple. Shown that the magnitude of the moment of a couple is given by Ƭ = Fd, where the symbols have their usual meanings.

Q.3

(c)

2009
Page 49 of 111 “Science Cannot Solve The Ultimate Mystery Of Nature. And That Is Because, In The Last Analysis, We Ourselves Are A Part Of The Mystery That We Are Trying To Solve.” Max Planck

TORQUE, ANGULAR MOMENTUM & EQUILIBRIUM CHAPTER # 5 Q.1

QUESTIONS

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Choose the correct answer for each from the given options:(iv) The angular momentum of a particle is conserved if the ___.  Net torque on the particle is zero  The acceleration of the particle is zero  Net force on the particle is zero  Net displacement of the particle is zero (i) The rate of change of angular momentum is also called ___.  Acceleration  Force  Torque  Power

2010
Q.1 Choose the correct answer for each from the given options:(i) Torque is defined as the time rate of change of ___.  Angular momentum  Linear momentum  Angular velocity  Angular acceleration (ii) Why does a slight push on an axle of a wheel not cause any motion? If the line of action of force passes through the axis of rotation then moment arm is zero and no torque is produced. This same happens here.
ARI F RAZA

Q.2 Ans.

2011
Q.1 Choose the most appropriate answer for each from the given options:(iii) The rate of change of angular momentum with respect to time is called ___.  Force  Angular velocity  Angular acceleration  Torque (iv) Two forces equal in magnitude but opposite in direction and not on the same line, constitute a ___.  Couple  Power  Circle  Force

Page 50 of 111 “Science Cannot Solve The Ultimate Mystery Of Nature. And That Is Because, In The Last Analysis, We Ourselves Are A Part Of The Mystery That We Are Trying To Solve.” Max Planck

TORQUE, ANGULAR MOMENTUM & EQUILIBRIUM CHAPTER # 5

NUMERICALS

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NUMERICALS
Q.1 A 12 m ( ) ladder weighing 400 N ( ) rests against a vertical wall at a point 10 m ( ) above the ground. The center of gravity of the ladder is one-half ( ) the way up. A man weighing 200 N ( ) climbs three-fourth ( ) up the ladder. Assuming that the wall is smooth, find the reaction of the ground ( ) and the wall ( ). Hint:-

(

)

ARI F RAZA

( )

( )

( )

√

√(

)

(

)

√

√

Q.2

(R=643.38 N, F=232.26 N) 1992 0 A ladder weighing 200 N ( ) rests against a smooth vertical wall at an angle of 60 ( ) with the ground. Its center rd of gravity is at of its length ( ) from the base. Find: (a) The frictional force ( ) which prevents the ladder from slipping; (b) The co-efficient of static friction ( ). Hint:; ( ) ( ) ( )

Page 51 of 111 “Not Only Does God Play Dice, But... He Sometimes Throws Them Where They Cannot Be Seen.” Stephen Hawking

TORQUE, ANGULAR MOMENTUM & EQUILIBRIUM CHAPTER # 5

NUMERICALS

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Q.3

(H=38.5 N, μ=0.1925) 1996 A uniform horizontal rod weighing 98 N ( ) is pivoted at a vertical wall. Its far end is supported by a string whose other end is fixed to a point on a wall above the pivot. A boy of mass 20 kg ( ) stands at the center of the rod. Find only the vertical component of the tens( ) ion in the string and only vertical component of the reaction at the pivot ( ). Length of the horizontal rod is 4 m ( ). Hint:;

ARI F RAZA

( ) ( )

( )

Q.4

Q.5

(Ty = 147 N, V = 147 N) 2000 A particle of mass 400 g ( ) rotates in a circular orbit of radius 20 cm ( ) with constant angular speed of 1.5 rev/sec ( ); calculate the magnitude of angular Momentum ( ) of particle with respect to the center of the orbit. ( ) Hint:(0.150 J.s) 2001 A 15 m ( ) ladder weighing 350 N ( ) rests against a smooth wall at a point 12 m ( ) above the ground. The center of gravity of the ladder is one-third ( ) the way up. A body of 470 N ( ) climbs half way ( ) up the ladder; calculate the reaction of wall ( ) and the ground ( ). Hint:-

( ( )

) ( )

( )

√

√(

)

(

)

√

√

Page 52 of 111 “Not Only Does God Play Dice, But... He Sometimes Throws Them Where They Cannot Be Seen.” Stephen Hawking

TORQUE, ANGULAR MOMENTUM & EQUILIBRIUM CHAPTER # 5

NUMERICALS

[e-mail]

Q.6

(F=263.75 N, R=861.37 N) 2002P/M 0 A ladder of length “L” and weight 200 N ( ) rests against a vertical wall at an angle of 50 ( ). The center of gravity of the ladder is “0.4L” ( ) from the base. How large a force of friction ( ) must exist at the base of ladder if it is not to slip? What is the necessary co-efficient of static friction ( ). Hint:; ( ) ( )
ARI F RAZA

( )

Q.7

(H=67.04 N, μ= 0.3352) 2003P/E A uniform ladder of length “L” and weight 60 N ( ) rests against a smooth vertical wall. If the co-efficient of friction between the ladder and the ground is 0.40 ( ), find the minimum angle ( ) such that the ladder may not slip. Hint:; ( ) ( ) ( ) ( )
( (

( ) ( )
) )

( ) ) ) ( )

(

)

( (

Page 53 of 111 “Not Only Does God Play Dice, But... He Sometimes Throws Them Where They Cannot Be Seen.” Stephen Hawking

TORQUE, ANGULAR MOMENTUM & EQUILIBRIUM CHAPTER # 5

NUMERICALS

[e-mail]

Q.8

Q.9

Q.9

(θmin= 51.3 ) 2003P/M A 15 m ladder weighing 350 N rests against a smooth vertical wall at a point 12 m above the ground. The center of gravity is one-third the way up. A boy of mass 47 kg climbs half up the ladder. Calculate the reaction exerted by the wall and the ground. Hint:- Same as Q.5 (F=263.75 N, R=861.37 N) 2009 A uniform ladder of length “L” and weight 50 N rests against a smooth a vertical wall. If the co-efficient of friction between the ladder and the ground is 0.40, find the minimum angle (θmin) such that the ladder may not slip. Hint:- Same as Q.7 0 (θmin= 51.3 ) 2010 A uniform ladder having length “L” and weighing 50 N, rests against a smooth a vertical wall. If the co-efficient of friction between the ladder and the ground is 0.40, find the minimum angle (θmin) such that the ladder may not slip. Hint:- Same as Q.7 0 (θmin= 51.3 ) 2011
ARI F RAZA

0

Page 54 of 111 “Not Only Does God Play Dice, But... He Sometimes Throws Them Where They Cannot Be Seen.” Stephen Hawking

GRAVITATION CHAPTER # 6

QUESTIONS

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QUESTIONS

1993
Q.3 Q.3 Q.3 Q. Q. Q. (a) (b) (c) Distinguish between “g” and “G”. State Newton’s law of gravitation. How does the value of “g” vary with altitude.

1994
Fill in blanks:(ix) The force of attraction acts along the line joining the two intersecting bodies. True and false:(viii) Weightlessness is overcome in space-craft by creating artificial gravity. (T) Choose the correct answer:(viii) A particle moving with a uniform speed in a circle has ___ acceleration.  Zero  Maximum  Uniform  None of these (ix) If the distance between the center of body and the center of Earth increases the value of “g” ___.  Increases  Decreases  Remains same  None of these
ARI F RAZA

1995
Q.3 Q.3 Q. (b) State Newton’s law of gravitation. (b) Discuss the variation of “g” with altitude and depth. True and false:(xii) The objects falling freely to the Earth move in the same direction. (F) (xv) The Moon is freely falling to Earth. (T) (xvi) An astronaut in spacecraft experience weightlessness because the Earth’s gravitational force ceases to act on him. (F)

1996
Q.4 Describe any two of the following:(i) Variation of “g” with depth and height; (ii) Weightlessness in satellites.

1997
Q.3 Q.3 Q.4 State and explain the Newton’s law of gravitation. Derive an equation for “g” corresponding to the depth of the Earth. (a) Two books are kept on a table separately. Explain “why they do not move towards each other by force of gravitation”. Write short notes on:(i) Artificial gravity. (a)

1998
Q.4 Write short notes on any two of the following:(iv) Weightlessness in satellites.

1999
Q.4 Write short notes on any two of the following:Page 55 of 111 “In Physics, You Don't Have To Go Around Making Trouble For Yourself - Nature Does It For You.” Frank Wilczek

GRAVITATION CHAPTER # 6 (ii) (iii) Q.4 (a) Weightlessness in satellites; Variation of “g” with depth and height.

QUESTIONS

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2000
True and false:(i) Weight of a body depends on the altitude of the location as well as on the motion of the frame of reference. (T) (ii) Difficulties in eating and drinking in spacecraft due to weightlessness can be removed by spinning spacecraft about its own axis. (T) (iii) Weight of body at the center of the Earth becomes zero. (T)

2001
Q.2 (a) Choose the correct answer:(iii) The apparent weight of a person standing in an elevator which is moving down with uniform acceleration will be ___.  Same as that on the surface of Earth  Greater than its weight on the surface of Earth  Less than its weight on the surface of Earth  None of these Discuss the variation of “g” with altitude or depth. Choose the correct answer:(iii) The apparent weight of a body in a satellite orbiting around the Earth is always ___.  Zero  mg  Increasing  None of them
ARI F RAZA

Q.2 Q.4

(c) (a)

2002P/E
Q.3 (a) Choose the correct answer:3 (iii) A helicopter of mass 3x10 kg rises vertically with a constant speed of 25 m/sec. What resultant force acts on the helicopter?  Zero  3 x 104 N upward  3 x 10 4 N downward  None of these State the Newton’s law of gravitation. Using this law obtain a relation for the average mass and density of the Earth.

Q.3

(b)

2002 P/M
Q.2 Q.3 (c) (a) Obtain a relation for the variation of “g” with depth. Choose the correct answer:(ii) Above the surface of Earth if we go to a distance equal to double the radius of the Earth the value of “g” will become ___.  One-ninth  One-third  One-fourth  One-half (iii) Artificial gravity is produced in a spacecraft to ___.  Increase the weight of the astronaut  Decrease the weight of the astronaut  Overcome the state of weightlessness  None of these Derive an expression for mass of the Earth. Page 56 of 111 “In Physics, You Don't Have To Go Around Making Trouble For Yourself - Nature Does It For You.” Frank Wilczek

Q.3

(b)

GRAVITATION CHAPTER # 6

QUESTIONS

[e-mail]

2003 P/E
Q.3 Q.3 (b) (a) Discuss the variation of “g” with depth.

2003 P/M
Choose the correct answer:(i) If the radius of the Earth were to shrink and its mass were to remains the same, the acceleration due to gravity on the surface of Earth will ___.  Decreases  Remains same  Increases  None State the Newton’s law of gravitation. Give the unit of “G” in SI system. What change will be produced in “G” if the mass of Earth is doubled? Choose the correct answer:(i) If a man goes to a height equal to the radius of Earth from its surface, his weight relative to that of Earth would become___.  Half  Same  Twice  One-fourth

Q.3 Q.4

(b) (a)

2004
ARI F RAZA

Q.3 Q.4 Q.3

(c) (c) (a)

How can artificial gravity be created to overcome the problem due to weightlessness? Deduce the variation of “g” with depth expression.

2005
Choose the correct answer:(iii) The ocean tides are caused by gravitational force exerted on Earth by ___.  Moon only  Sun only  Both Moon and Sun  None What is the cause of weightlessness in a satellite orbiting round the Earth? Show that a block suspended from the ceiling of an elevator through a spring balance will become weightless if the cable holding the elevator suddenly breaks.

Q.3

(c)

2006
Q.2 Q.3 (c) (a) How is artificial gravity created in an orbiting spacecraft? Derive the relevant expression. Choose the correct answer:(iii) The weight of an object in a satellite orbiting round the Earth is equal to the ___.  Actual weight  Greater than the actual weight  Less than the actual weight  Zero Discuss the variation of “g” with depth and derive the relevant mathematical expression.

Q.3 Q.2

(c) (a)

2007
Choose the correct answer:(iii) The apparent weight of a body in a satellite orbiting round the Earth is ___.  Increasing  Decreasing  Zero  None Page 57 of 111 “In Physics, You Don't Have To Go Around Making Trouble For Yourself - Nature Does It For You.” Frank Wilczek

GRAVITATION CHAPTER # 6 Q.3 Q.3 (b) (a)

QUESTIONS Derive the relation for the variation of “g” with altitude.

[e-mail]

2008
Choose the correct answer:(iii) If we go up from the surface of the Earth to a distance equal to the radius of Earth, the value of “g” will be ___.     Derive an expression for the variation of “g” with depth.

Q.4 Q.1

(b)

2009
Choose the correct answer for each from the given options:(xi) A man goes up to a height from Earth’s surface equal to the radius of the Earth. His weight relative to the Earth’s surface would ___.  Become half  Remains same  Become double  Become one-fourth (iii) How is artificial gravity created in orbiting space-craft? Obtain the relevant mathematical expression for it. (xiv) How would the weight of the body vary as it is taken from the Earth to the Moon? What will be the effect on its mass? The weight of a body will decrease 6 times as value of “g” is six times less on Moon as compared to Earth. The mass of body will remain the same.
ARI F RAZA

Q.2 Q.2 Ans.

2010
Q.1 Choose the correct answer for each from the given options:(v) If we go up from the surface of the earth to a distance equal to the radius of earth, the value of “g” will become ___.  One-fourth  One-eighth  One-ninth  Double (vii) Show by calculation why the acceleration due to gravity at the center of earth is zero. Also calculate the mass of the earth. The value of “g” at depth “d” from the surface of Earth is calculated as:( ) ( ) . / . /

Q.2 Ans.

2011
Q.1 Select the most appropriate answer for each from the given options:(v) If one moves up from the surface of the earth to a distance equal to the radius of the earth, the value of acceleration due to gravity will be ___.     How is weightlessness experienced in a satellite overcome? Explain.

Q.2

(xi)

Page 58 of 111 “In Physics, You Don't Have To Go Around Making Trouble For Yourself - Nature Does It For You.” Frank Wilczek

GRAVITATION CHAPTER # 6

NUMERICALS

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NUMERICALS
Q.1 A man weighing 60 kg ( ) is standing on the floor of an elevator. Calculate the force ( ) exerted by the man on the floor of the elevator when it:( ) ( )  Is at rest; Hint:( ) ( )  Descends at the constant speed of 4 m/s; Hint:2  Moves up with an acceleration of 2 m/s ; ( ) ( ) Hint:2 Moves down with an acceleration of 2 m/s ; ( ) ( ) Hint:(588 N, 588 N, 708 N, 468 N) 1993 At what distance from the center of the Earth ( ) does the gravitational acceleration have one-third the value ( ) that it has on Earth. Hint:( ) ( ) ( ) ( )

Q.2

√

√

√

ARI F RAZA

Q.3

(11.084 x 10 m or 1.732 Re) 1993 Find how deep ( ) from the surface of Earth a point is where the acceleration due to gravity is half ( the value on Earth’s surface. Hint:. / . / . /

6

) of

Q.4

(Re/2) The radius of Moon is 27% ( 1.2% .

1995 ) of the radius of the Earth ( ) and its mass is )?

/ of the mass of the Earth ( ). Find the gravitational acceleration on the Moon ( What will be the weight of a body of 980 N ( ) on the surface of Moon ( )? Hint:(a)
( ) ( )

(b) Q.5 (1.60 m/s , 160 N) The planet Jupiter has a mass ( ) 314 times ( times( ) larger than that of the Earth ( ( ). Hint:2

1997 ) that of the Earth ( ). Its radius ( ) is 11.3 ); find the acceleration due to gravity on the surface of Jupiter

Page 59 of 111 “Knowledge Itself Is Power.” Sir Francis Bacon

GRAVITATION CHAPTER # 6
( ( ) )

NUMERICALS

[e-mail]

Q.6

Q.7

(24.10 m/s ) 2002 P/E The radius of Moon is 27% of the radius of the Earth and its mass is 1.2% of the mass of the Earth. Find the gravitational acceleration on the Moon Hint:- Same as Q.4 2 (1.61 m/s ) 2002 P/M At what distance ( ) from the center of the Earth does the gravitational acceleration have one-half ( ) of the value it has on the surface of the Earth? Hint:( ) ( ) ( ) ( )

2

√
6

√

√

Q.8

(9.049 x 10 m OR 1.414 Re) 2003 P/E 27 30 The planet Jupiter of mass 2 x 10 kg ( ) revolves around the Sun of mass 2 x 10 kg ( ) in a circular orbit of 11 radius 7.8 x 10 m ( ); Calculate the gravitational force ( ) between them and the orbital speed ( ) of Jupiter. Hint:- (a) ( ) (b)
√
23 3

√ √ √

√

Q.9

(4.385 x 10 N, 13.076 x 10 m/s) If the two chambers of a spacecraft are connected to a tunnel of 30 m (
ARI F RAZA

2003 P/M ), calculate

the spin frequency ( ) to produce the artificial gravity in spacecraft. Hint:Q.10
√ √ √

Q.11

Q.12

(7.72 rev/min) 2004 At what depth ( ) from the surface of Earth is the value of acceleration due to gravity becomes one-fourth ( ) the value at the Earth’s surface. Hint:- Same as Q.3 6 (3/4Re OR 4.8 x 10 m) 2004 At what distance ( ) from the center of the Earth does the value of “g” become half ( ) of the value it has on the surface of Earth. Hint:- Same as Q.7 6 (9.049 x 10 m OR 1.414Re) 2005 Suppose a new planet “X” is discovered with a diameter ( ) 10 times ( ) bigger as compared to that of Earth ( ) and has mass ( ) equal to 300 times ( ) that of Earth ( ). Compute the gravitational acceleration ( ) at the surface of the planet “X”. Hint:( ( ) )

(29.4 m/s )

2

2008

Page 60 of 111 “Knowledge Itself Is Power.” Sir Francis Bacon

Work, Power And Energy CHAPTER # 7

QUESTIONS

[e-mail]

1992
Q.4 (a) Define the following terms:(i) Work; (ii) Energy; (iii) Absolute potential energy. Derive an expression for the absolute potential energy of a body lying at the:(i) Surface of Earth; (ii) At a height “h”.

Q.4

(b)

1993
Q.4 Q.4 (a) (b) Define energy. Distinguish between potential energy and kinetic energy. Give two examples of each. Fill in blanks:(i) The Momentum of a body becomes doubled and its kinetic energy becomes four times when its velocity is doubled. (ii) 1 joule/second = 1 watt (iii) 1hp = 550 ft.lb/sec
ARI F RAZA

1994
Q.3 Q.3 Q. (a) What is energy? State and explain the law of conservation of energy. Give its two examples. (b) Derive work energy equation. Fill in blanks:2 (v) Einstein’s mass-energy equation is E = mc . 6 (ii) One kilowatt hour (kWh) = 3.6 x 10 J. True and false:(iii) Work done in a gravitational field is independent of path. (T) Choose the correct answer:(iii) Friction is a self-adjusting force.  It increases indefinitely with the external force  It does not increase indefinitely with the external force  It remains constant  None of these (v) A pendulum bob is swinging with simple harmonic motion. Its potential energy is maximum at ___.  Extreme positions  Mean position  At any position along the path  None of these

Q. Q.

1995
Q. Q. Fill in the blanks:(i) Watt-hour is the unit of work. True or false:(xiv) A body possesses gravitational potential energy only when it exists in the Earth’s or some other body’s gravitational field. (T) (xvii) Both the center of mass and center of gravity of a body are at one and the same point in a uniform gravitational field. (T)

1996
Page 61 of 111 “I Think Therefore I Am.” Rene Descartes

Work, Power And Energy CHAPTER # 7 Q.4 Q.4 (a) (ii) (b) Fill in blanks:6 One kilowatt hour = 3.6 x 10 J. Describe any two of following:(iii) Work-energy equation.

QUESTIONS

[e-mail]

1997
Q.4 Write short notes on:(iii) Work-energy equation.

1998
Q.4 Write short notes on:(iii) Absolute gravitational potential energy.

1999
Q.3 Q.3 Q.2 (a) (b) (a) What is energy? State and explain the law of conservation of energy. Give two examples. Derive work-energy equation.

2001
Choose the correct answer:(ii) Which of following is not the unit of power?  Kilowatt-hour  Horse power  Foot .lb/sec  J/sec Choose the correct answer:(i) When the direction of force is opposite to the direction of displacement, then the work done will be ___.  Positive  Negative  Zero  None of these Define conservative field. Prove that the gravitational field is a conservative field.
ARI F RAZA

Q.4

(a)

Q.4 Q.4

(b) (a)

2002 P/E
Choose the correct answer:(ii) The absolute P.E of a body of mass “m” in the Earth’s gravitational field is given by ___.     (iii) Which of the following is not the unit of power?  Kilowatt  Kilowatt-hour  Horsepower  Ft.lb/sec Define the terms potential energy and kinetic energy. A body of mass “m” is projected up in to the air vertically in the Earth’s gravitational field with a velocity “V”. It attains a height “h”. Establish a relation for the kinetic energy possessed by the body.

Q.4

(b)

2002 P/M
Q.4 Q.2 (b) (a) Explain the term work and gives its dimensions and three of its units.

2003 P/E
Choose the correct answer:Page 62 of 111 “I Think Therefore I Am.” Rene Descartes

Work, Power And Energy CHAPTER # 7 (i) Watt-hour is the unit of ___.  Force  Acceleration  Energy  Velocity

QUESTIONS

[e-mail]

Q.3

(a)

Q.4 Q.4 Q.3

(b) (c) (a)

If ⃗ = ̂ - ̂ and ⃗ = ̂ + ̂, then work done will be ___.  4J  8J  2J  12J Choose the correct answer:(i) One horse power is equal to ___ W.  400  580  746  70 Define a conservative field. Prove that the gravitational field is a conservative field. (ii)

2003 P/M
Prove that the gravitational field is a conservative field.

2004
ARI F RAZA

Q.4

(a)

Q.4

(c)

Choose the correct answer:(i) Kilowatt-hour is a unit of ___.  Energy  Power  Time  None of these Choose the correct answer:(iii) Work done by centripetal force is always ___.  Positive  Zero  Negative  None of these Define work. Give its SI units. Establish work-energy equation for a free falling body in a gravitational field.

2005
Q.2 Q.3 (c) (a) Establish work-energy equation. Choose the correct answer:(ii) Power is equal to ___.     Q.4 (a)
⃗ ⃗

Choose the correct answer:(iii) If mass and speed both are doubled, the kinetic energy of a moving body ___.  Increases 4 times  Increases 6 times  Increases 8 times  Remains same Page 63 of 111 “I Think Therefore I Am.” Rene Descartes

Work, Power And Energy CHAPTER # 7

QUESTIONS

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2006
Q.2 (a) Choose the correct answer:(ii) In case of negative work the angle between the force and the displacement is ___.  00  900  1800  450

2007
Q.3 (a) Choose the correct answer:(i) The dot product of force and velocity is ___.  Work  Power  Energy  Momentum State and prove the law of conservation of energy for the free fall motion. Choose the correct answer:(iii) The work done by a conservative force along a closed path is ___.  Positive  Negative  Zero  None
ARI F RAZA

Q.3 Q.4

(c) (a)

2008
Q.2 Q.4 (c) (a) Define a conservative field. Show that the gravitational field is a conservative field. Choose the correct answer:(i) The work done by centripetal force “F” on a body moving in a circle is zero because ___.  The body moves parallel to F  The body moves opposite to F  The body moves at right angle to F  The centripetal & centrifugal forces balance each other Establish work-energy equation.

Q.4 Q.1

(c)

2009
Choose the correct answer for each from the given options:(vi) The dimensions of kinetic energy are ___.  ML2T-2    Q.1 ML2T-2 ML2T2 ML2T-1

2010
Choose the correct answer for each from the given options:(vi) When a body moves vertically upward, the work done will be ___.  Positive  Negative  Zero  maximum (b) Establish Work-Energy equation.

Q.5 Q.1

2011
Select the most appropriate answer for each from the given options:(vi) The work done by a conservative force along a closed path is ___. Page 64 of 111 “I Think Therefore I Am.” Rene Descartes

Work, Power And Energy CHAPTER # 7

QUESTIONS

[e-mail]

(xv)

Q.2 Ans.

(viii)

 Positive  Negative  Zero  None of these If the speed of a moving body is halved, its kinetic energy becomes ___.  One fourth  Half  Three times  Four times Prove that power is the scalar product of force and velocity.

ARI F RAZA

Page 65 of 111 “I Think Therefore I Am.” Rene Descartes

Work, Power And Energy CHAPTER # 7

NUMERICALS

[e-mail]

Q.1

A small sphere of mass 50 g ) is suspended by a light string. As it oscillates the sphere is 1.75 m ( ) from the ground at its highest point and 0.75 m ( ) at its lowest point. Find its maximum speed ( ) and maximum momentum ( ). Hint:-

(a)
( ( √ √ ( ) ) √ ) ( ( ) )

(b)

ARI F RAZA

Q.2

(4.42 m/s, 0.221 N.s) Calculate the work done ( ) by a force given by ⃗ = ̂ position B. The position vectors of A and B are: ⃗ A= ̂ (⃗⃗⃗ ⃗⃗⃗ ) ( ) Hint:⃗⃗⃗ ⃗⃗⃗ ( ̂
( ) (⃗⃗⃗ ⃗⃗⃗ ) ( ̂ ̂ ̂) ( ̂ ̂ ̂)

̂) ( ̂ ̂) ̂ ̂ ̂ ( ̂) ( ̂) ( ̂) ( ̂) ( ̂ ) ( ̂ )

1993 ̂ in displacing a body from the position A to the ̂ ̂ + ̂ and ⃗ B= ̂ ̂+ ̂
̂ ̂

Q.3

Q.4

(44 J) 1994 ̂ in displacing the body from the position A to the ⃗ = ̂ Calculate the work done by a force given by ̂ ̂ and ⃗ B= ̂ ̂ position B. The position vectors of A and B are: ⃗ A= ̂ ̂ ̂ Hint:- Same as Q.2 (22 J) 1999 A ball of mass 100 g ( ) is thrown up in the air vertically and reaches a height of 9.8 m ( ); calculate the velocity ( ) with which it is thrown and its initial kinetic energy ( ). (Neglect air friction and take 2 g=10 m/s ) Hint:( )

(a)
√ √ √

(b) (14 m/s, 9.8 J)

2002 P/E

Page 66 of 111 “I Would Never Die For My Beliefs Because I Might Be Wrong.” Bertrand Russell

Work, Power And Energy CHAPTER # 7 Q.5

NUMERICALS

[e-mail]

A car weighing 9,800 N ( ) is moving at 25 m/s ( ). If the frictional force on it is 2000 N ( ), how fast ( ) is the car moving when it has traveled 60 m ( )? Hint:( ( √ ) ( ) √ √ √ √ ) ( ) √ √( )

Q.6

(19.62 m/s) 2007 A water pump is needed to lift water through a height of 2.5 meters ( ) at the rate of 500 gm/minute ( ). What will be the minimum horse power ( pump? ( ) Hint:-

) of the

Q.7

(0.273 x 10 hp) 2010 A water pump is needed to lift water through a height of 2.5 m ( ) at a rate of 500 gm/minute ( ). Find its minimum power in horse power ( Hint:- Same as Q.6 -3 (0.273 x 10 hp) 2011
ARI F RAZA

-3

)?

Page 67 of 111 “I Would Never Die For My Beliefs Because I Might Be Wrong.” Bertrand Russell

Wave Motion And Sound CHAPTER # 8

GOVT DEGREE COLLEGE S.R.E MAJEED,KARACHI QUESTIONS

[e-mail]

1992
Q.5 Q.5 Q.5 (a) (b) (c) State the basic conditions for a frictionless system to execute simple harmonic motion. A particle is moving with a uniform speed along the circumference of a circle. Show that the motion of its projection along one of its diameters is simple harmonic. Derive expressions for the:(i) Time period; and (ii) Instantaneous and maximum velocity of the projection of a particle along one of the diameters of circle of reference. Explain Newton’s formula for the speed of sound in a material medium. Which factors forced Laplace to correct Newton’s formula for speed of sound waves in a material medium? Explain Laplace correction.

Q.6 Q.6

(a) (b)

1993
Q.5 Q.5 (a) (b) Define simple harmonic motion. Give at least two examples of it. The time period changes /does not change during simple harmonic motion if mass of the bob is doubled in the following cases:(i) A bob is attached to an elastic spring; (ii) A bob is attached to an inelastic string. What are the characteristics of musical sound? Differentiate between intensity and loudness of sound. How are they related? Define and explain intensity level. Describe its units.
ARI F RAZA

Q.6 Q.6 Q.4 Q.4

(a) (b) (a) (b)

1994
What is the principle of superposition of waves? Two sinusoidal waves with the same amplitude, frequency and wavelength travels in opposite directions. Calculate the point of maximum and minimum amplitudes. What are these points called and what is the distance between them in terms of wavelength? Write short notes on any two of the following:(i) Simple pendulum; (ii) Speed of sound and Laplace's correction; (iii) Sonometer and the laws of vibration on a stretched string. True and false:(ii) There is no effect of change of temperature on velocity of sound. (F) (vi) An oscillatory motion is one in which the acceleration is proportional to the force is called simple harmonic motion. (F) (vii) The time period of simple pendulum depends upon the length of the pendulum. (T) (ix) Beats are produced due to the superposition of two waves of the same frequency. (F) Choose the correct answer:(x) Motion under elastic restoring force is called ___.  Simple harmonic motion  Circular motion  Linear motion  None of these

Q.5

Q.

Q.

1995
Q.4 Q.4 (a) (b) Define simple harmonic motion? What is simple pendulum? Show that the motion of a simple pendulum is simple harmonic. Derive its time Page 68 of 111 “Ignorance Is Never Better Than Knowledge.” Enrico Fermi

Wave Motion And Sound CHAPTER # 8

GOVT DEGREE COLLEGE S.R.E MAJEED,KARACHI QUESTIONS

[e-mail]

Q.4 Q.5

Q.5 Q.

Q.

Q.

period expression. What will be the trajectory of the bob of a vibratory simple pendulum after it has got suddenly detached from the thread while passing through its mean position? (a) Draw spherical wave crests initiating from a source of sound represented by a dot and a listener represented by another dot a few centimeter away. Then derive expressions for the frequency heard by a listener when:(i) The listener is moving towards the source sound at rest; (ii) The source of sound moving towards the listener at rest. (c) What are shock waves? Explain. Fill in blanks:(iii) The distance between two adjacent nodes is . (vi) The velocity of sound waves in vacuum is zero. Choose the correct answer:(xxiv) A stretched string between two fixed points is vibrating in one segment. The frequency generated is called ___. st  1 overtone  Fundamental frequency  Normal harmonics  None of these (xxv) The loudness of sound depends upon ___.  Wavelength  Frequency  Amplitude  None of these (xxvi) When the temperature of air raises the speed of sound increases because ___.  Frequency of wave increases  Both the frequency and the wavelength increases  Only wavelength increases  None of these (xxix) When a sound source moves towards a stationary listener, there is ___.  An apparent increase in wavelength  An apparent increase in frequency  A decrease in pitch  None of these True and false:(xviii) Sound wave can’t be polarized. (T) (xix) If two tuning forks of 100 Hz and 120 Hz are sounded together, the number of beats heard per second will be 20. (T) (d)
ARI F RAZA

1996
Q.5 (a) Q.6 (a) Define simple harmonic motion. Show that the motion of projection of uniform circular motion of a particle on the diameter of the reference circle is simple harmonic. Hence find the expressions for displacement, velocity, acceleration and time period of a simple harmonic oscillator. (i) Fill in the blanks:(a) Decibel is the unit of intensity level. (b) Sound waves which have frequency more than 20,000 Hz are called Ultrasonic waves. (ii) Choose the correct answer:(a) The characteristic of a musical sound which distinguish between the notes of the same pitch and intensity is known as ___.  Quality  Loudness  Intensity level Page 69 of 111 “Ignorance Is Never Better Than Knowledge.” Enrico Fermi

Wave Motion And Sound CHAPTER # 8

GOVT DEGREE COLLEGE S.R.E MAJEED,KARACHI QUESTIONS

[e-mail]

Q.6

(b)

 None of these Sound waves travels fastest in ___.  Air  Water  Iron  None of these What are standing waves? Derive expressions for the frequencies of vibration in a stretched string when it vibrates in:(i) One loop; (ii) Two loops; (iii) Three loops. Name the instrument used in the laboratory for studying such vibrations. (b)

1997
Q.5 (a) Choose the correct answer:(i) The velocity of sound waves ___.  Increases with increase in temperature  Decrease with increase in temperature  Doesn’t change with increase or decrease of temperature  None of these (ii) The sound waves are ___.  Longitudinal  Transverse  Medium are not made of material  None of these In a medium derive the Newton’s formula for the velocity of sound. What correction did Laplace’s make in this formula. What are the characteristics and conditions of simple harmonic motion. Show that the motion of simple pendulum is simple harmonic motion and derive an expression for its time period.
ARI F RAZA

Q.5 Q.6 Q.6

(b) (a) (b)

1998
Q.5 (a) (i) (ii) (iii) Fill in the blanks: Internationally recognized unit of loudness is Sone. State whether the following statement is True or False:The velocity of sound waves increases with temperature. Choose the correct answer:The velocity of a wave of wavelength “λ” and frequency “ ” is given by ___.     Q.5 (b) λ (T)

Q.6

(a)

 None of them Define simple harmonic motion and show that the motion of projection of uniform circular motion of a particle on the diameter of a reference circle is simple harmonic. Derive the expressions for:(i) Displacement; (ii) Velocity; (iii) Time period; (iv) Frequency. (i) Fill in the blanks: The maximum number of beats that a human ear can detect is 7. Page 70 of 111 “Ignorance Is Never Better Than Knowledge.” Enrico Fermi

Wave Motion And Sound CHAPTER # 8 (ii)

GOVT DEGREE COLLEGE S.R.E MAJEED,KARACHI QUESTIONS

[e-mail]

Q.6

(b)

True and false: The stationary waves are produced due to the superposition of two identical waves traveling in opposite directions. (T) (iii) Choose the correct answer: In aerodynamics the ratio of the velocity of the sound waves to the velocity of the sound source is called ___.  Beats  Mach number  Harmonics  None of these What is Doppler’s effect? Derive the expressions for the frequency when:(i) The source is approaching the stationary listener; (ii) The source and the listener both are approaching each other.

1999
Q.5 (a) Q.5 (b) Fill in the blanks:(i) Decibel is the unit of intensity level of sound. (ii) Sound waves which have more than 20000 Hz of frequency are called Ultrasonic. Choose the correct answer:(i) The characteristic of musical sound which distinguishes between the notes of the same pitch and intensity is known as ___.  Quality  Loudness  Intensity level  None of these (ii) Sound waves travels fastest in ___.  Air  Water  Iron  None of these What are standing waves? Derive expressions for the frequencies of vibration in a stretched string when it vibrates in:(i) In loop; (ii) Two loops; (iii) Three loops. What is Doppler’s effect? Discuss the Doppler’s effect for the following possibilities:(i) When the listener is moving and the source is at rest; (ii) When the source is moving and the listener is at rest; (iii) When both the source and the listener are moving.
ARI F RAZA

Q.5

(c)

Q.6 Q.6

(b) (b)

2000
Q.5 (a) Choose the correct answer:(i) When the speed of jet plane becomes greater than the speed of sound then loud sound produced is due to ___.  Shock waves  Standing waves  None of these (ii) For good acoustics of a hall, reverberations should not be ___.  Too small  Too large  None of these (iii) Maximum beat frequency which human ear can detect is ___. Page 71 of 111 “Ignorance Is Never Better Than Knowledge.” Enrico Fermi

Wave Motion And Sound CHAPTER # 8

GOVT DEGREE COLLEGE S.R.E MAJEED,KARACHI QUESTIONS

[e-mail]

Q.5

(b)

Q.5 Q.6

(b) (a)

Q.6

(b)

 3  5  7  None of these (iv) Pitch of sound depends upon ___.  Intensity  Loudness  Frequency  None of these (i) A body of mass “m” is attached to one end of a spring which lies on a frictionless horizontal surface whose other end is fixed. The body is allowed to move under elastic restoring force. What type of motion will it execute? Derive an expression for its acceleration. (ii) Show that for smaller amplitude the motion of simple pendulum is simple harmonic. True and False:(i) A motion which repeats itself in equal intervals of time is called periodic motion. (T) (ii) Frequency of infrasonic waves is greater than 2000 Hz. (F) (iii) In standing waves nodes is the point of maximum displacement. (F) (iv) Loudness of sound depends on the intensity and auditory sensation. (T) (i) What is the Newton’s formula for the speed of sound? Discuss Laplace’s correction in it. (ii) What is the effect of temperature on speed of sound? Derive formula showing relation between speed of sound and absolute temperature of the medium.
ARI F RAZA

2001
Q.5 (a) Choose the correct answer:(i) Which of the following represents compressional waves?  Sound waves  Light waves  Radio waves  X-rays (ii) The distance between the nodes and anti-nodes in a loop is ___.     (iii)  None The frequency of the transverse stationary waves produced in a string of a Sonometer is “f”. If only the tension in the string of the Sonometer is doubled, the new frequency will be ___.   √  λ

Q.5 Q.5 Q.6

(b) (c) (a)

  None of these A particle is moving along a circular path with a constant angular velocity. Show that its projection on one of its diameter executes simple harmonic motion. A string of length “l” is stretched between two hooks. Find the frequency of stationary waves produced in string when vibrating in a loop, two loops, three loops and in “n” loops. Choose the correct answer:(i) A decibel is a ___.  Musical instrument  Measure of intensity level Page 72 of 111 “Ignorance Is Never Better Than Knowledge.” Enrico Fermi

Wave Motion And Sound CHAPTER # 8

GOVT DEGREE COLLEGE S.R.E MAJEED,KARACHI QUESTIONS

[e-mail]

Q.6 Q.6

(b) (c)

 Wavelength  Musical note (ii) Beats are the result of ___.  Diffraction  Constructive and destructive interference  Constructive interference only  None of these (iii) Speed of sound waves does not depend upon ___.  Wind speed  Temperature  Pressure  Density of the medium What is Doppler’s effect? Derive an expression for the apparent frequency heard by a stationary listener when the source is moving towards him. Name the characteristics of musical sound. Define intensity of sound, loudness of sound and intensity level. Write down Weber-Fechner’s law.

2002P/E
Q.5 (a) Choose the correct answer:(i) A 252 Hz tuning fork produces four beats per second when sounded with another tuning fork of unknown frequency?  63 Hz  256 Hz  108 Hz  248 Hz (ii) We recognize the voice of a friend over the telephone by the ___ of sound.  Quality  Intensity  Loudness  Pitch (iii) The acceleration of free fall on the Moon is of that on the Earth. What would be the period on
ARI F RAZA

the Moon of a simple pendulum which has a period of 1 second on the Earth?    √  Define simple harmonic motion. Derive an expression for the acceleration of a body attached with a spring lying on a smooth horizontal frictionless surface executing simple harmonic motion. What is the Newton’s formula for the speed of sound? Discuss Laplace’s correction in it. Choose the correct answer:(i) When stationary waves are set up in a stretched string, it has a fundamental frequency of 1000 Hz. What would be the new fundamental frequency if the tension in the wire is increased four times?  980 Hz  500 Hz  1010 Hz  2000 Hz (ii) When the temperature of air rises, the speed of sound wave increases because ___. Only frequency increases Only wavelength increases Both wavelength and frequency increases. Page 73 of 111 “Ignorance Is Never Better Than Knowledge.” Enrico Fermi
√

Q.5 Q.5 Q.6

(b) (c) (a)

Wave Motion And Sound CHAPTER # 8

GOVT DEGREE COLLEGE S.R.E MAJEED,KARACHI QUESTIONS

[e-mail]

Q.6

(b)

Q.6

(c)

Only wavelength decreases. The frequency of oscillation of a simple pendulum depends upon ___.  Mass of the bob  Amplitude of vibration  Length of pendulum  None of them What are stationary waves? A string of length “l ” is stretched between two hooks. Find the frequency of the stationary waves produced in the string when it is vibrating in one loop, two loops, three loops and “n” loops. What is simple pendulum? Show that its motion is simple harmonic when the amplitude is sufficiently small. (iii)

2002 P/M
Q.5 (a) Choose the correct answer:13 (i) The relative intensity . / for the sound of a jet engine is 10 . The intensity level in dB will be ___.  13  1300  130  1.3 (ii) A spring mass system is oscillating with simple harmonic motion with the time period “T”. If we double the mass of its bob, the new time period will be ___.  T  2T  1.414T  0.707T (iii) Which of the following frequencies of sound wave is audible?  5 Hz  5000 Hz  25000 Hz  50 KHz Show the motion of simple pendulum is simple harmonic. Mention Newton’s formula for the speed of sound. Describe Laplace’s correction in it. Choose the correct answer:(i) If a string is vibrating in its fundamental mode, then to excite to the next higher mode, the tension must be ___.  Halved  Doubled  Tripled  Quadrupled (ii) Supersonic jets may produce a double sonic boom due to two shock waves within the time interval of ___.  0.02 sec  0.1 sec  0.001 sec  0.21 sec How can standing waves be produced? Give their characteristics. What are Beats? Derive a relation for Beat frequency.
ARI F RAZA

Q.5 Q.5 Q.6

(b) (c) (a)

Q.6 Q.6 Q.5

(b) (c) (a)

2003 P/E
Choose the correct answer:(i) Beats are produced due to ___. Page 74 of 111 “Ignorance Is Never Better Than Knowledge.” Enrico Fermi

Wave Motion And Sound CHAPTER # 8

GOVT DEGREE COLLEGE S.R.E MAJEED,KARACHI QUESTIONS

[e-mail]

Q.5 Q.5 Q.6

(b) (c) (a)

Q.5 Q.5 Q.5

(b) (c) (a)

 Diffraction  Interference  Polarization  Refraction (ii) The unit of intensity level of sound is ___.  Watt  Joule  Decibel  Diopter (iii) If the mass of the bob of a simple pendulum is replaced by another bob of double mass but of the same size; its time period ___.  Increases  Decreases  Remains the same  Becomes infinity Prove that the motion of projection of a particle in uniform circular motion is simple harmonic on one of the diameters of the reference circle. Discuss the variations in the pitch of sound when a source of sound moves towards a stationary listener. Choose the correct answer:(i) Supersonic waves have the frequency of more than ___.  20 Hz  2,000 Hz  50,000 Hz  20,000 Hz -12 2 (ii) The intensity level of sound of intensity 10 W/m in bell is ___.  Zero  One  Two  Three  None of these (iii) When two exactly similar waves travel in a medium in opposite directions, they produce ___.  Standing waves  Beats  Resonance  Diffraction State three laws of transverse vibrations on a stretched string in a Sonometer. What are Beats? How are they produced? Obtain an expression for the beat frequency.
ARI F RAZA

2003 P/M
Choose the correct answer:(i) The time period of a simple pendulum depends upon ___.  Length  Amplitude  Mass of the bob  Wavelength (ii) The physical quantity which is related to the loudness of sound is ___.  Frequency  Intensity  Quality  Temperature (iii) An object is executing simple harmonic motion. Its kinetic energy is maximum at ___.  Mean position Page 75 of 111 “Ignorance Is Never Better Than Knowledge.” Enrico Fermi

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Q.5 Q.5 Q.6

(b) (c) (a)

Q.6 Q.6

(b) (c)

 Extreme positions  At any point along the path  None of these Derive an expression for the time period of a simple pendulum. A particle is moving with uniform speed along the circumference of a circle. Prove that the motion of its projection along one of the diameters is simple harmonic. Choose the correct answer:(i) When two vibrating bodies have slightly different frequencies, they produce ___.  Echo  Beats  Resonance  Polarization (ii) Which of the following properties of sound is affected by change in temperature?  Amplitude  Wavelength  Frequency  Intensity (iii) If the tension in the string is made four times, the speed of transverse waves will be ___.  Half  Doubled  Four times  The same Distinguish between musical sound and noise. What is Doppler’s effect? Derive the expressions for the apparent frequency when an observer move towards and away from the stationary source.
ARI F RAZA

2004
Q.5 (a) Choose the correct answer:(i) If the mass of the bob of a simple pendulum is doubled, its time period will ___.  Be doubled  Be half  Remains constant  None of these (ii) The value of elastic restoring force in case of a spring is ___.     (iii) The frequency of a second’s pendulum is ___.  1 Hz  2 Hz  0.5 Hz  None of these Derive the expression for the instantaneous velocity of projection of a particle moving with uniform velocity on the circumference of a circle. Define the following terms:(i) Intensity of sound; (ii) Loudness; (iii) Intensity; (iv) Quality of sound. Choose the correct answer:(i) The pitch of sound depends upon ___. Page 76 of 111 “Ignorance Is Never Better Than Knowledge.” Enrico Fermi

Q.5 Q.5

(b) (c)

Q.6

(a)

Wave Motion And Sound CHAPTER # 8

GOVT DEGREE COLLEGE S.R.E MAJEED,KARACHI QUESTIONS

[e-mail]

Q.6 Q.6

(b) (c)

 Velocity  Intensity  Frequency  None of these (ii) Which of the following is a compressional wave?  Light wave  Sound wave  Radio wave  None of these (iii) If two tuning forks of frequencies 256 Hz and 260 Hz are sounded together, the number of beats heard per second will be ___.  3  4  5  8 Explain Newton’s formula for the speed of sound. How did Laplace’s correct it? What is the effect of temperature on the speed of sound. Derive relevant expression. Derive the expressions for the frequency of a stationary wave produced in a stretched string vibrating in:(i) One loop; (ii) Two loops; (iii) Three loops; (iv) “n” loops.
ARI F RAZA

2005
Q.5 (a) Choose the correct answer:(i) If the bob of a vibrating pendulum is suddenly detached from the string at its mean position, its path will be ___.  A straight line  A circle  A parabola  A hyperbola (ii) Human ears can hear sound waves having frequency ___.  5 Hz  5,000 Hz  25,000 Hz  50,000 Hz (iii) The velocity of sound in a gas increases with ___.  Temperature  Pressure  Loudness  Frequency Define simple harmonic motion. Prove that for a small amplitude of vibration, the motion of simple pendulum is simple harmonic. What is Doppler’s effect? Obtain an expression for the apparent frequency heard by a listener when he moves with a velocity “v” towards a stationary sound source emitting waves of frequency “ ”. Choose the correct answer:(i) Frequencies which are multiples of fundamental frequency are called ___.  Beat frequencies  Nodal frequencies  Harmonics  Doppler frequencies (ii) Which of the following is not the property of sound waves? Page 77 of 111 “Ignorance Is Never Better Than Knowledge.” Enrico Fermi

Q.5 Q.5 Q.6

(b) (c) (a)

Wave Motion And Sound CHAPTER # 8

GOVT DEGREE COLLEGE S.R.E MAJEED,KARACHI QUESTIONS

[e-mail]

Q.6 Q.6

(b) (c)

 Interference  Diffraction  Polarization  Refraction (iii) “Sone” is the unit of ___.  Intensity level  Intensity of sound  Loudness of sound  Quality of sound Explain the phenomenon of Beats. Obtain an expression for the Beat frequency for the waves describe by the following:, ; where the symbols have their meanings. What are stationary waves? On factors do the frequency of stationary waves in a stretched string depends?

2006
Q.5 (a) Choose the correct answer:(i) Beats are produced due to ___.  Diffraction  Interference  Polarization  Refraction (ii) Which of the following represents longitudinal waves?  Light waves  Sound waves  Radio waves  X-rays (iii) The distance between consecutive nodes of a stationary wave is ___.  λ 
ARI F RAZA

 Q.5 Q.5 Q.6 (b) (c) (a)  Prove that the motion of projection of a particle in a uniform circular motion is simple harmonic on one of the diameters of the reference circle. Consider the spring mass system to show that its energy remain constant throughout its motion. Choose the correct answer:(i) The maximum number of beats per second that a human ear can detect is ___.  5  7  3  4 (ii) One Sone at 1000 Hz is equal to ___.  60 dB  40 dB  30 dB  100 dB (iii) The Earthquake waves are the examples of ___.  Audible waves  Infrasonic waves  Shock waves  Ultrasonic waves Explain Newton’s formula for the speed of sound in air and discuss Laplace’s correction in it. Page 78 of 111 “Ignorance Is Never Better Than Knowledge.” Enrico Fermi

Q.6

(b)

Wave Motion And Sound CHAPTER # 8 Q.6 (c)

GOVT DEGREE COLLEGE S.R.E MAJEED,KARACHI QUESTIONS

[e-mail]

Derive the formula for the apparent frequency heard by a stationary listener when the source of sound is moving towards the listener.

2007
Q.5 (a) Choose the correct answer:(i) Decibel is the unit of ___.  Wavelength  Speed of wave  Intensity level  Frequency (ii) The speed of sound is highest in ___.  Solid  Gas  Liquid  Vacuum (iii) The voice of the two persons having the same pitch and loudness can be recognized due to the characteristic of the sound known as ___.  Beats  Quality  Frequency  Intensity Prove that the motion of a simple pendulum is simple harmonic when the angle of its swing is very small. Explain the phenomenon of Beats. Obtain an expression for the Beat frequency for the waves describe by the following:, ; where the symbols have their meanings. Choose the correct answer:(i) The pitch of sound depends upon ___.  Frequency  Wavelength  Intensity  Velocity (ii) If the mass of a body suspended from a spring is doubled, the period of vibration of the body becomes ___.  Double  Half  √  Four times  None of these (iii) The maximum number of beats that can be heard by a human ear is ___.  3  5  7  9  None of these Derive the expression for the instantaneous velocity of a projection of a particle (point) moving with uniform speed on the circumference of a circle. What is Doppler’s effect? Derive the expression for the apparent frequency when the source of sound is moving away from the stationary listener.
ARI F RAZA

Q.5 Q.5 Q.6

(b) (c) (a)

Q.6 Q.6

(b) (c)

2008
Q.5 (a) Choose the correct answer:(i) The frequency of a simple pendulum is given by ___.

Page 79 of 111 “Ignorance Is Never Better Than Knowledge.” Enrico Fermi

Wave Motion And Sound CHAPTER # 8    (ii)

GOVT DEGREE COLLEGE S.R.E MAJEED,KARACHI QUESTIONS √ √ √

[e-mail]

Q.5 Q.5

(b) (c)

Q.6

(a)

Q.6 Q.6

(b) (c)

 None of these Beats are produced due to ___.  Diffraction  Interference  Polarization  Refraction (iii) When the temperature of air rises, the speed of sound increases because ___.  The frequency of the wave increases  The wavelength of the wave increases  Both the wavelength & frequency increases  Neither the wavelength nor the frequency increases What are the conditions for SHM? Show that the motion of projection of a particle in a uniform circular motion is simple harmonic on one of the diameters of the reference circle. What are stationary (or standing) waves? A string of length” l ” is stretched between two hooks; find the frequency of the stationary waves produced in the string when it is vibrating in:(i) One loop; (ii) Two loops; (iii) Three loops. Choose the correct answer:(i) If you go on increasing the stretching force on a guitar, its frequency of vibration ___.  Increases  Decreases  Neither decrease nor decrease  Becomes zero (ii) If the mass of a body suspended from a spring is increased to 4 times, the period of vibration of the body will become ___.  4 times  2 times  √  (iii) If the fundamental frequency of vibration of a string fixed at both ends is 50 Hz, the fourth harmonic will be ___.  100 Hz  50 Hz  200 Hz  250 Hz Show that the total energy of a body attached to an elastic spring and executing SHM remains the same everywhere. Define intensity of sound & loudness. Give Weber-Fechner law and explain the intensity level with its units.
ARI F RAZA

2009
Q.1 Choose the correct answer for each from the given options:(v) A body executes simple harmonic motion if ___.   Page 80 of 111 “Ignorance Is Never Better Than Knowledge.” Enrico Fermi

Wave Motion And Sound CHAPTER # 8

GOVT DEGREE COLLEGE S.R.E MAJEED,KARACHI QUESTIONS

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(viii)

(xii)

(xv)

(xvii)

Q.2
Ans.

(vi)

 √  The S.I. unit of intensity of sound is ___. 2  Watt/m  Decibel  Weber  Diopter If two tuning forks with frequencies 256 Hz and 262 Hz are sounded together, the beat frequency will be ___.  3  4  5  6 If the tension in a stretched string is increased 4 times, the speed of the transverse wave in it will increase ___.  4 times  8 times  2 times  16 times The velocity of sound has maximum value in ___.  Solids  Liquids  Gases  Free space Why did Newton’s formula for the speed of sound in air fail? Who corrected this formula? Describe the discrepancy and give the corrected formula.
ARI F RAZA

Newton assumed the propagation of sound through air is an Isothermal process while in actual it was an adiabatic process, that’s why his formula could not meet the experimental results and failed. Laplace’s corrected his formula.

Q.2
Ans.

(xv)

A wire hangs from the dark tower so that the upper end is not visible. How can we determine the length of the wire?
√ to calculate the length of wire.

Note the time period for one oscillation and then use

Q.4 Q.5

(b) (a)

OR What is the difference between interference and beats of sound waves? Elaborate it. What is Doppler’s effect? Explain this effect analytically when the source of sound moves away from a listener at rest. Write three applications of Doppler’s effect. A particle is in a state of uniform circular motion. Prove that its projection of motion along any one of the diameters circle executes simple harmonic motion.

2010
Q.1 Choose the correct answer for each from the given options:(viii) Which of the following does not exhibit Simple Harmonic Motion?  A hanging spring supporting a weight  The balance wheel of a watch  The wheel of an automobile  The string of a violin (ix) Pitch depends upon ___.  Frequency  Loudness  Time period  Distance (x) The velocity of sound in space is ___. Page 81 of 111 “Ignorance Is Never Better Than Knowledge.” Enrico Fermi

Wave Motion And Sound CHAPTER # 8

GOVT DEGREE COLLEGE S.R.E MAJEED,KARACHI QUESTIONS

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Q.2
Ans.

(i)

 332 m/sec  334 m/sec  330 m/sec  Zero If the tension in the string is doubled, what will be the effect on the speed of standing waves in the string?
√ √ √ (√ ) √ ( )

Q.5

(b)

Define simple Harmonic Motion and prove that for a small amplitude of vibration the motion of a simple pendulum is simple harmonic motion. Also derive the formula for its time period.

2011
Q.1 Select the most appropriate answer for each from the given options:(i) If two tuning forks with frequencies 256 Hz and 262 Hz are sounded together, the number of beats per second will be ___.  3  4  5  6 (ix) Earthquake waves are the examples of ___.  Audible waves  Infrasonic waves  Ultrasonic waves  Shock waves (xvii) This is a compressional wave ___.  Light wave  Sound wave  Radio waves  X-rays (iii) For simple harmonic motion, will the time period change or not, by doubling the mass of the bob attached to: (a) Elastic spring; (b) Inelastic spring? Explain.
ARI F RAZA

Q.2
Ans.

(a)

√

√

√ (

√ )

√ ( )

(b)

√

Q.3 Q.5

(b) (b)

A particle is in a state of uniform circular motion. Prove that its projection along one of its diameters executes simple harmonic motion. What is Doppler’s effect? Explain this effect analytically when the source of sound moves away from a listener at rest. Write three applications of Doppler’s effect.

Page 82 of 111 “Ignorance Is Never Better Than Knowledge.” Enrico Fermi

Wave Motion And Sound CHAPTER # 8

NUMERICALS

[e-mail]

Q.1

Find the velocity ( ) of sound in a gas in which two waves of wavelength 0.80 m ( ) and 0.81 m ( ) produced 5 beats ( ) per second. Hint:. / . / . /
. / . / ( )

Q.2

(324.67 m/sec) 1992 A simple pendulum completes 4 vibrations ( ) in 8 sec ( ) on the surface of Earth ( ). Find the time period on the surface of Moon ( ) where the acceleration due to gravity is one-sixth ( ) as that on Earth. Hint:√ √
( ) ( )

√

√

Q.3

(4.9 sec) -12 2 Calculate the intensity level ( ) of the faintest audible sound when I = 10 W/m . ( ) Hint:. / . /
ARI F RAZA

1993

Q.4

(0 dB) 1993 A stationary wave is set in a 1.5 m ( ) long string fixed at both ends. The string vibrates in five segments ( ) when driven by a frequency of 100 Hz ( ). Calculate the wavelength ( ) and the fundamental frequency ( ). Hint:- (a) (b)

Q.5

(20 Hz, 0.6 m) Calculate the length ( ) of second’s pendulum ( gravity is 0.167 ( ( ) Hint:√ ( )

1994 ) on the surface of Moon where the acceleration due to ) times that on the surface of Earth.

Q.6

(0.165 m) 1995 A source of sound and listener are moving towards each other with velocities which are 0.5 times ( 0.2 times ( ) the speed of sound respectively. If the source is emitting 2 kHz ( ) tone, calculate the frequency heard by the listener ( ). Hint:. / . / . / (4.8 kHz) 1995

) and

Page 83 of 111 “Science Is Organized Knowledge. Wisdom Is Organized Life.” Immanuel Kant

Wave Motion And Sound CHAPTER # 8 Q.7

NUMERICALS

[e-mail] ). Determine its period ( ) of

When a mass “m” is hung in a vertical spring it stretches through 6 cm ( vibration if it is pulled down a little and then released. Hint:√ √ √

Q.8

(0.483 sec) 1996 A guitar has a linear density of 7.16 g/cm ( ) and is under tension of 152 N ( ). The fixed supports of the string are 89.4 cm ( ) apart. If it vibrates in three segments ( ), calculate the wave speed ( ), the wavelength ( ) and the frequency of the standing waves ( ). Hint:ARI F RAZA

√

√

√

Q.9

(14.57 m/s, 0.595 m, 24.44 Hz) 1996 5 2 3 Find the velocity ( ) of sound in air at atmospheric pressure “P” 1.01 x 10 N/m ( ), density (ρ) = 1.2 kg/m and γ = 1.40. Hint:√ √ √ √

Q.10

(343.26 m/s) 2 Calculate the length ( ) of a second’s pendulum at a place where g = 10 m/s . ( ) Hint:√ ( ) (1.012 m) A body of mass 0.5 kg ( ) is attached to a spring is displaced from its equilibrium position and is released. If the spring constant “K” is 50 N/m, find:(i) Time period ( ); Hint:(ii) Hint:√ √ √

1997

1997

Q.11

Frequency.

(0.628 sec, 1.59 Hz) “Science Is Organized Knowledge. Wisdom Is Organized Life.” Immanuel Kant

1998 Page 84 of 111

Wave Motion And Sound CHAPTER # 8 Q.12

NUMERICALS

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A car has a siren sounding 2 kHz ( ) tone. What frequency ( ) will be detected by a stationary listener as the car is approaching him at 80 km/h ( ). Hint:. / . / . / (2142 Hz) 1998 A standing wave is established in 110 m ( ) long string fixed at both ends. The string vibrates in four segments ( ) when driven at 110 Hz ( ). Determine the wavelength ( ) and fundamental frequency ( ). Hint:(55 m, 27.5 Hz) 1999 A car has been sounding a 4 kHz ( ) tone. What frequency ( ) will be detected by a stationary listener as the car approaches him at a speed of 50 km/h ( )? Hint:. / . / . / (4172 Hz) Find the length ( ) of the second’s pendulum ( ) on planet Jupiter where the value of “g” is 2.63 times ( ) the value of “g” on Earth’s surface. Hint:√
( ) ( )

Q.13

Q.14

1999

Q.15

Q.16

(2.610 m) 0 Find the speed ( ) of sound in air at 0 C ( “M” = 0.0288 kg/mol and R = 8.314 J/mol.K. Hint:√ √ √ √

2000 ); given γ = 1.40 for air, molecular mass of air

ARI F RAZA

Q.17

Q.18

(332.16 m/s) 2000 The frequency of a string is 125 Hz ( ) when it is vibrating in 5 segments ( ) (nodes at both ends). Calculate the frequency when the string vibrates in three ( ) and four segments ( ). What is the speed ( ) of the wave in it, if the length of the string is 0.80 m ( )? Hint:(75 Hz, 100 Hz, 40 m/s) 2001 An ambulance has a siren sounding at a frequency of 2000 Hz ( ) and moving towards a stationary listener standing at a bus stop. If the frequency heard by the listener is 2150 Hz ( ); find the speed ( ) of the ambulance. (Speed of sound in air is 340 m/s). Hint:. / (22.24 m/s) 2001 A body hanging from a spring is set in to motion and the period of oscillation is found to be 0.80 sec ( ). After the body has come to rest, it is removed. How much shorter ( ) will the spring be when it comes to rest? ( ) Hint;√ ( )

Q.19

(0.1588 m or 15.88 cm) “Science Is Organized Knowledge. Wisdom Is Organized Life.” Immanuel Kant

2002 P/E Page 85 of 111

Wave Motion And Sound CHAPTER # 8 Q.20

NUMERICALS

[e-mail] ) where a simple pendulum 1.5 m ( ) long

Compute the acceleration due to gravity on the surface of Moon ( makes 100 vibrations ( ) in 605 sec ( ). Hint:√
2
( ( ) )

Q.21

(1.61 m/s ) Calculate the speed ( ) of sound in air at S.T.P ( 0 sound at 37 C ( )? Hint:√ √ √ √ √ √ √ √

2002 P/E ). What will be the speed of

Q.22

(332 m/s, 353.74 m/s) 2002 P/M A 2 m ( ) long string with mass 0.004 kg ( ) is stretched horizontally by passing one end over a pulley and attaching a 1 kg ( ) mass to it; find the speed ( ) of the transverse waves in the string and the frequency ( ) of the fifth ( ) harmonic. Hint:√ √(
)

√(

)

√

√

Q.23

(70 m/s, 87.5 Hz) A source of sound and listener are moving towards each other with velocities 0.5 times ( 0.2 ( ) times the speed of sound respectively. If the source is emitting 2 kHz ( calculate the frequency ( ) heard by the listener. Hint:. / . / . /
ARI F RAZA

2002 P/M ) and ) tone,

Q.24

Q.25

Q.26

(4.8 kHz) 2003P/E A string 2 m long and of mass 0.004 kg is stretched horizontally by passing one end over a pulley and attaching a 1 kg mass to it; find the speed of the transverse waves in the string and the frequency ( ) of the second ( ) harmonic. Hint:- Same as Q.22 (70 m/s, 35 Hz) 2003 P/E A mass at the end of a spring oscillates with simple harmonic motion with a period of 0.40 sec ( ); find the acceleration ( ) when the displacement is 4.0 cm ( ). ( ) ( ) Hint:. / ( ) 2 (- 9.86 m/s ) 2003 P/M Two cars moving straight to each other from opposite directions with the same speed ( ). The horn of one is blowing with the frequency of 3000 Hz ( ) and is heard by the people in the other car with the frequency of 3400 Hz ( ); find the speed of the cars ( ) if the speed of sound in air is 340 m/s ( ). Hint:. / . / . / . /
( )

Q.27

(21.20 m/s) 2003 P/M The period of vibration of a body of mass 25 g ( ) attached to a spring, vibrating on a smooth horizontal surface, when it is displaced 10 cm ( ) to the right of its mean position is 1.57 sec ( ) and the velocity at the end of this displacement is 0.4 m/s ( ). Determine:(i) Spring constant ( ); (ii) Total energy ( ); (iii) Amplitude ( ). Hint:- (i) (ii)
√
( ( ) )

(

)

(

)

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Wave Motion And Sound CHAPTER # 8

NUMERICALS

[e-mail]

(iii)
-3

√

√

√

√

√

√

Q.28

Q.29.

(0.4 N/m, 4 x 10 J, 0.1414 m) 2004 A standing wave is established in a 2.4 m ( ) long string fixed at both ends. The string vibrates in four ( ) segments when driven at 200 Hz ( ). Determine:(i) Wavelength; Hint:(ii) The fundamental frequency. Hint:(1.2 m, 50 Hz) 2004 A car has its siren sounding 2 kHz ( ) tone. If the frequency heard by the stationary listener is 2143 Hz ( ); find the speed ( ) with which it approaches the stationary listener. (The speed of sound ( ) in air is 332 m/s). Hint:. / (22.16 m/s) 2005 In a Sonometer a wire of length 1 m ( ) when plucked at the center vibrates with a frequency of 250 Hz ( ); calculate the wavelength ( ) and speed ( ) of the waves in the wire. Hint:(2 m, 500 m/s) 2005 Find the length of the second’s pendulum on the planet Jupiter where the value of “g” is 2.63 times that of the “g” on the surface of Earth. Hint:- Same as Q.15 (2.610 m) 2006 0 Find the speed of sound in air at the temperature of 27 C ( ), given γ = 1.42, R = 8.314 J/mol/K and -3 molecular mass of air is M = 28.8 x 10 kg/mol.
ARI F RAZA

Q.30

Q.31

Q.32

Hint:Q.33

√

√

√

√

(350.68 m/s) 2006 The time period of a pendulum is 2 sec ( ) at the surface of Earth; calculate its time period on the surface of Moon ( ) where the value of acceleration due to gravity is one-sixth ( ) that of the value of “g” at the surface of Earth. Hint:√ √
( ) ( )

√

√

Q.34

Q.35

(4.9 sec) 2007 A car has its siren sounding 2 kHz tone. If the frequency heard by a stationary observer is 2143 Hz, find the speed with which the car approaches the stationary observer. (Speed of sound in air = 332 m/s). Hint:- Same as Q.29 (22.16 m/s) 2007 A note of frequency 650 Hz ( ) is emitted from an ambulance. What frequency ( ) will be detected by a listener if the ambulance moves? (Speed of sound = 340 m/s) (i) At the speed of 15 m/s ( ) from the listener; Hint:. / . / . / (ii) At the speed of 18 m/s ( ) towards the listener. Hint:. / . / . /

Q.36

(622.5 Hz, 686.4 Hz) 2008 A body of mass 32 g ( ) is attached to an elastic spring and executes SHM. Its velocity is 0.4 m/s ( )when the displacement is 8 cm ( ) towards right. If the spring constant is 0.4 N/m ( ). Calculate:Page 87 of 111 “Science Is Organized Knowledge. Wisdom Is Organized Life.” Immanuel Kant

Wave Motion And Sound CHAPTER # 8 (i) Total energy ( Hint:(ii) Hint:-3

NUMERICALS );
( ) ( )

[e-mail]

The amplitude of its motion ( ).
√ √ √ √ √ √

Q.37

Q.38

Q.39

(3.84 x 10 J and 0.1385 m) 2008 The time period of a simple pendulum is 2 seconds on the surface of Earth. Calculate its time period on the surface of Moon where the acceleration due to gravity is one-sixth that of its value on the Earth’s surface. Hint:- Same as Q.33 (4.9 sec) 2009 A Sonometer wire of length 1 m, when plucked at the center, vibrates with a frequency of 250 Hz. Calculate the wavelength and the speed of the waves in the wire. Hint:- Same as Q.30 (2 m, 500 Hz) 2009 A note of frequency 500 Hz ( ) is being emitted by an ambulance moving towards a listener at rest. If the listener detects a frequency of 526 Hz ( ), calculate the speed ( ) of the ambulance. Take the speed of the sound at room temperature to be 340 m/s ( ). Hint:. / (16.81 m/s) 2009 A string 2 meters ( ) long and mass 0.004 kg ( ) is stretched horizontally by passing one of its ends over a pulley and the string is attached with one kg ( ) mass to it vertically. Find the speed ( ) of the transverse wave on the string and the frequency of the fundamental ( ) and fifth harmonic ( ) at which the string will vibrate.
ARI F RAZA

Q.40

Hint:Q.41

√

√(

)

√(

)

√

√

Q.42

(70 m/s, 17.5 Hz, 87.5 Hz) 2010 A simple pendulum completes 4 vibrations in 8 seconds on the surface of the Earth. Find the time period on the surface of the Moon where the acceleration due to gravity is one-sixth as that of the Earth. (4.9 sec) Hint:- Same as Q.2 A note of frequency 500 Hz ( ) is being emitted by an ambulance moving towards a listener at rest. If the listener detects a frequency of 526 Hz ( ), calculate the speed ( ) of the ambulance. (Speed of the sound is 340 m/s at that moment ( ). Hint:- Same as Q.39 (16.81 m/s) 2011

Page 88 of 111 “Science Is Organized Knowledge. Wisdom Is Organized Life.” Immanuel Kant

NATURE OF LIGHT CHAPTER # 9

GOVT. DEGREE COLLEGE S.R.E MAJEED, KARACHI. QUESTIONS

[e-mail]

1992
Q.7 Q.7 Q.8 (a) What do you mean by interference of light? Give the conditions of interference of light waves. (b) Discuss Young’s double-slit experiment to measure the wavelength of the light. Write short notes on any of the following:(i) Wave front and Huygens’s principle; (ii) Polarization of light.

1993
Q.8 Write short notes on any of two following:(i) Diffraction grating; (ii) Polarization of light.

1994
ARI F RAZA

Q.6 Q.6 Q. Q. Q.

(a) What are Newton’s ring? They prove an important property of light. What is this property? (b) Show how Newton’s ring can be used to find the radius of curvature of a lens? Fill in the blanks:(vii) From the phenomenon of polarization it is proved that light waves are transverse. True and false:(x) One of the conditions for interference of light is that sources of light must be in phase coherence. (T) Choose the correct answer:(vii) Electromagnetic waves consist of an oscillatory electric field “E” and an oscillatory magnetic field “B”; both fields are ___. Parallel to each other Parallel to the direction of propagation of waves Perpendicular to each other None the these

1995
Q.6 Q.6 Q.7 (a) (b) What is interference of light? Describe Young’s double-slit experiment for demonstrating the phenomenon of interference of light. Derive the expression for fringe spacing. Write short notes on any of the following:(i) Interference of light; (iv) Diffraction of light. Fill in the blanks:(viii) The ability of light waves to bend around the edges of obstacles in their path is called diffraction. True and false:(xviii) Sound waves can’t not be polarized. (T) Choose the correct answer:(xxvii) A monochromatic light beam is entering from one medium in to another. Which one the following properties remains unchanged?  Amplitude  Velocity  Wavelength Page 89 of 111 “Science Is What You Know. Philosophy Is What You Don’t Know.” Bertrand Russell

Q. Q. Q.

NATURE OF LIGHT CHAPTER # 9

GOVT. DEGREE COLLEGE S.R.E MAJEED, KARACHI. QUESTIONS

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(xxx)

 Frequency Colors in soap bubbles is due to ___.  Polarization  Interference  Reflection  None of these

1996
Q.7 (a) (i) (ii) Fill in the blanks: Maxwell concluded that light waves are electromagnetic in nature.  Interference of light can be explained on the basis of wave theory of light. Choose the correct answer: Which of the following phenomenon can’t be explained by the wave theory of light?  Interference  Diffraction  Photoelectric effect  None of these  In the Newton’s rings the central dark spot is always ___.  Bright  Dark  Red  None of these
ARI F RAZA

Q.7

(b)

What is the difference between Fresnel and Fraunhofer diffraction? Explain. Describe a diffraction grating. How it can be used to find the wavelength of sodium light?

1997
Q.8 Q.8 (a) (b) Illustrate the conditions for “Interference of light”. For the radius of Newton’s rings derive an expression of the relation between the radius of curvature of lens and wavelength of light .

1998
Q.7 (a) (i) Fill in the blanks: In Michelson’s Interferometer the moveable mirror is moved to produce a path difference of .  The bending of light waves around the sharp edges of an obstacle is called diffraction of light. Choose the correct answer: The structure of a crystal can be studied with the help of ___ of X-rays.  Interference  Diffraction  Polarization  None of these OR Fill in the blanks: Two absolutely identical waves starting from the same point are said to be in phase. True and false: The interference and diffraction patterns are exactly the same. (F) Choose the correct answer: The phenomenon of ___ proves that light waves are transverse in nature.  Refraction  Reflection  Polarization Page 90 of 111 “Science Is What You Know. Philosophy Is What You Don’t Know.” Bertrand Russell

(ii)

(i) (ii) (iii)

NATURE OF LIGHT CHAPTER # 9

GOVT. DEGREE COLLEGE S.R.E MAJEED, KARACHI. QUESTIONS

[e-mail]

Q.7 Q.8

 Interference What is interference of light? Describe Young’s double-slit experiment for demonstrating the interference phenomenon. Derive the expression for fringe spacing. Write short notes on any of following:(i) Polarization of light. (b)

1999
Q.7 Q.7 Q.8 (a) What are Newton’s rings? Give experimental arrangement for producing Newton’s rings. (b) Derive an expression for the radius of curvature of the lens used in the arrangement. Write short notes on any of following:(i) Polarization of light.

2000
Q.7 (a) Choose the correct answer:(i) When light (white) passes through thin films, colors are formed due to ___.  Diffraction  Dispersion  Interference  Both interference and diffraction (ii) Photoelectric effect proves that light consists of ___.  Particles  Waves  Both particles and waves  None of these (iii) Polarization of light due to tourmaline crystals takes place because of ___.  Reflection  Selective absorption  Refraction  None these (iv) When both point source and the screen are placed at finite distance from the diffracting obstacle the phenomenon is called ___.  Fresnel diffraction  Fraunhofer diffraction  Both Fresnel diffraction & Fraunhofer diffraction  None of these (a) (i) Explain how Young’s double-slit experiment proves that interference effect takes place in case of light waves. (a) (ii) Derive expression for fringe spacing in Young’s double-slit experiment. Write short notes on any two of following:(iii) Diffraction grating; (iv) Michelson’s Interferometer.
ARI F RAZA

Q.7 Q.7 Q.8

2001
Q.7 (a) Choose the correct answer:(i) Diffraction is a special type of ___.  Reflection  Refraction  Interference  Polarization (ii) In Michelson’s Interferometer, semi-silvered plate is used to obtain ___.  Dispersion  Phase coherence  Monochromatic light  Unpolarized light Page 91 of 111 “Science Is What You Know. Philosophy Is What You Don’t Know.” Bertrand Russell

NATURE OF LIGHT CHAPTER # 9 (iii)

GOVT. DEGREE COLLEGE S.R.E MAJEED, KARACHI. QUESTIONS

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Q.7 Q.8

(b) (a)

Q.8

(b)

Which of the following is not electromagnetic wave?  X-rays  Radio waves  Ultraviolet  α-rays th How are Newton’s ring formed? Derive an expression for the radius of n bright Newton’s rings? Choose the correct answer:(i) The condition for interference in thin films is reversed because of ___.  Small thickness of films  Refraction  Phase reversal  Diffraction (ii) Which of the following demonstrates the transverse nature of light waves?  Interference  Polarization  Diffraction  Refraction What is diffraction grating? Give an expression for the determination of the wavelength of a monochromatic source by diffraction grating.

2002 P/E
Q.7 (a) Choose the correct answer:(i) The transverse nature of light can be verified by ___.  Interference  Diffraction  Polarization  Refraction (ii) Which of the following equation represents Bragg’s law?  
ARI F RAZA

Q.7 Q.8

(b) (a)

Q.8

(b)

  What is meant by constructive and destructive interference? Explain Young’s double-slit experiment and obtain expressions for the position of bright and dark fringes. Choose the correct answer:(ii) The characteristic property of light which does not change with medium is ___.  Frequency  Wavelength  Velocity  None of these Give the construction and working of Michelson’s Interferometer. How it is used to determine the wavelength of a monochromatic light?

2002 P/M
Q.7 (a) Choose the correct answer:(i) Light possesses ___.  Transverse nature  Electromagnetic character  Dual nature  All of these (ii) The evidence of transverse nature of light is provided by ___.  Polarization  Diffraction Page 92 of 111 “Science Is What You Know. Philosophy Is What You Don’t Know.” Bertrand Russell

NATURE OF LIGHT CHAPTER # 9

GOVT. DEGREE COLLEGE S.R.E MAJEED, KARACHI. QUESTIONS

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Q.7 Q.8

(c) (a)

Q.8

(b)

 Interference  Dispersion Describe the construction and working of the Michelson’s Interferometer. Choose the correct answer:(i) In thin films, destructive interference occurs when the path difference is ___.  An odd multiple of half wavelength  Only an even multiple of wavelength  An integral multiple of wavelength  None of these (ii) The number of lines ruled per cm on a diffraction grating is 4000. Its grating element is ___m.  2.5 x 10-4  2.5 x 10-6  4 x 103  4 x 105 Differentiate between the following:(i) Fresnel and Fraunhofer diffraction; (ii) Constructive and destructive interference.

2003 P/E
Q.7 (a) Choose the correct answer:(i) The appearance of colors in soap bubbles is due to ___.  Polarization  Diffraction  Refraction  Interference (ii) If a single lens is placed close to the eye, it is being used as ___.  Compound microscope  Telescope  Simple microscope  Spectrometer (iii) In thin film interference the positions of constructive interference and destructive interference are changed due to ___. Phase coherence Phase reversal Diffraction Interference Differentiate between interference and diffraction patterns. Choose the correct answer:(ii) The bending of light around the sharp corners of an obstacle is called ___. Interference Polarization Diffraction Refraction Describe diffraction grating. How it can be used to determine wavelength of a monochromatic light? (Derive a relevant mathematical expression).
ARI F RAZA

Q.7 Q.8

(c) (a)

Q.8

(b)

2003 P/M
Q.7 (a) Choose the correct answer:(i) Electromagnetic waves consist of oscillatory electric field and magnetic field, both are ___.  Parallel to each other  Parallel to the direction of light waves propagation  Perpendicular to each other  None of these Page 93 of 111 “Science Is What You Know. Philosophy Is What You Don’t Know.” Bertrand Russell

NATURE OF LIGHT CHAPTER # 9 (ii)

GOVT. DEGREE COLLEGE S.R.E MAJEED, KARACHI. QUESTIONS

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Q.7 Q.8

(c) (a)

Q.8

(b)

A monochromatic beam of light is entering from one medium to another. The property which remains unchanged is ___.  Amplitude  Velocity  Frequency  Wavelength (iii) The bending of light around the obstacles is called ___.  Interference  Polarization  Diffraction  Refraction What is Newton’s rings? Derive an expression for the wavelength of light used in Newton’s rings. Choose the correct answer:(i) Light year is a unit of ___.  Distance  Time  Energy  Intensity (ii) The dispersion of white light after passing through a prism is due to ___. Different intensities Different amplitudes Different temperatures Different wavelengths What are the necessary conditions to observe the interference of light? Differentiate between interference and diffraction patterns.
ARI F RAZA

2004
Q.7 (a) Choose the correct answer:(i) The characteristic property of light which does not change with the medium is ___.  Frequency  Wavelength  Velocity  None of these (ii) In Young’s double-slit experiment, the fringe spacing is ___     None of these Which of the following phenomenon cannot be explained by the wave theory?  Interference  Diffraction  Photoelectric effect  None of these Give the construction of Michelson’s Interferometer. Draw a neat diagram. How it can be used to determine the wavelength of light? Choose the correct answer:(iii) The condition for the interference in a thin film is reversed because of ___.  Small thickness  Phase reversal  Refraction  None of these What is the difference between Fresnel and Fraunhofer diffractions? Derive Bragg’s law for X-ray (iii) Page 94 of 111 “Science Is What You Know. Philosophy Is What You Don’t Know.” Bertrand Russell

Q.7 Q.8

(b) (a)

Q.8

(b)

NATURE OF LIGHT CHAPTER # 9 diffraction.

GOVT. DEGREE COLLEGE S.R.E MAJEED, KARACHI. QUESTIONS

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2005
Q.7 (a) Choose the correct answer:(i) Colors in thin soap films are due to ___.  Reflection  Diffraction  Interference  Scattering (ii) To replace a bright fringe by the next bright fringe in Michelson’s Interferometer the moveable mirror is moved through a distance equal to ___.      None of these (iii) Which property of light is used to determine the concentration of an optically active substance such as sugar?  Interference  Dispersion  Diffraction  Polarization Define “Wave front”. State and explain Huygens’s principle. Describe Young’s double-slit experiment and obtain an experiment for the position of bright fringes on the screen. Choose the correct answer:(iii) The wave theory of light cannot explain ___.  Polarization  Photoelectric effect  Interference  Dispersion
ARI F RAZA

Q.7 Q.7 Q.8

(b) (c) (a)

2006
Q.7 (a) Choose the correct answer:(ii) In thin films interference, the position of constructive interference and destructive interference are interchanged due to ___.  Phase coherence  Interference  Phase reversal  Diffraction (iii) If 2000 lines/cm is ruled on a grating, its grating element is ___.  5 x 10-4 m  5 x 10-5 m  5 x 10-6 m  5 x 10-7 m Describe Young’s double-silt experiment and obtain an expression for the position of first bright fringe. Choose the correct answer:(i) Light year is a unit of ___.  Energy  Time  Distance  Intensity Define diffraction grating? How it is used to determine the wavelength of a monochromatic light? Derive Page 95 of 111 “Science Is What You Know. Philosophy Is What You Don’t Know.” Bertrand Russell

Q.7 Q.8

(b) (a)

Q.8

(b)

NATURE OF LIGHT CHAPTER # 9

GOVT. DEGREE COLLEGE S.R.E MAJEED, KARACHI. QUESTIONS

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the mathematical expression?

2007
Q.7 (a) Choose the correct answer:(i) Wave fronts near the point source is ___.  Plane  Cylindrical  Spherical  None of these (iii) The phenomenon of light which proves light waves are transverse is ___.  Reflection  Diffraction  Refraction  Polarization What is diffraction grating? How it is used to determine the wavelength sodium light? Derive the relevant mathematical expression. Choose the correct answer:(i) The condition for interference in a thin film is reversed because of ___.  Diffraction  Phase coherence  Refraction  Phase reversal (ii) Diffraction of X-rays can be studied by using ___.  A thin film  Diffraction grating  Rock salt  None of these Describe the experimental arrangement for observing Newton’s rings. Derive an expression for the radius th of n bright ring.
ARI F RAZA

Q.7 Q.8

(b) (a)

Q.8

(c)

2008
Q.7 (a) Choose the correct answer:(ii) The transverse nature of light was confirmed by ___.  Interference  Diffraction  Polarization  Dispersion (iii) The conditions for the constructive and destructive interference are reversed in case of thin films due to ___.  Phase reversal of one part of the wave  Phase reversal of both parts of the wave  Phase reversal of none  Change in frequency of waves Using Young’s double-slit arrangement obtain an expression for the position of bright fringes. Also calculate the bright fringe spacing Choose the correct answer:(iii) Yellow light from a sodium lamp is used to from Newton’s rings. The central spot in Newton’s rings will be ___.  Yellow  Bright  Dark  Neither bright nor dark What is the difference between Fresnel and Fraunhofer diffraction? Derive Bragg’s law for X-ray diffraction. Page 96 of 111 “Science Is What You Know. Philosophy Is What You Don’t Know.” Bertrand Russell

Q.7 Q.8

(b) (a)

Q.8

(c)

NATURE OF LIGHT CHAPTER # 9

GOVT. DEGREE COLLEGE S.R.E MAJEED, KARACHI. QUESTIONS

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2009
Q.5 Q.1 (b) Describe the young’s double-slit experiment and the formula for fringe-spacing.

2010
Choose the correct answer for each from the given options:(xii) In Young’s double-slit experiment, the condition for constructive interference is that the path difference must be ___.  An odd multiple of the half wavelength  An odd multiple of the whole wavelength  An integral multiple of the wavelength  An even number of the wavelength (iv) What is Interference of light? Give the difference of Fresnel’s and Fraunhoffer’s diffraction. (a) What is Diffraction of light and what is diffraction grating? Derive an expression for the wavelength of light by diffraction grating.

Q.2 Q.4

2011
Q.1 Select the most appropriate answer for each from the given options:(x) The wave theory of polarization cannot explain ___.  Polarization  Photoelectric effect  Interference  Diffraction (xvi) Electromagnetic waves consist oscillating electric and magnetic fields, both are ___.  Parallel to each other  Perpendicular to each other  Non-parallel to each other  None the these (v) Why are X-rays not diffracted by diffraction grating or thin films?
ARI F RAZA

Q.2 Ans.

X-rays are electromagnetic radiation of the order of slits, thin films, etc must be of the order of obstacle or aperture wavelength of light used.

wavelength. In order to diffract X-rays the obstacle or aperture in the form of or even less. Only then observable diffraction will be obtained. As a general rule

Q.4

(b)

Describe Young’s double slit experiment. Derive the relevant expression and the formula for fringe spacing.

Page 97 of 111 “Science Is What You Know. Philosophy Is What You Don’t Know.” Bertrand Russell

NATURE OF LIGHT CHAPTER # 9

NUMERICALS

[e-mail]

Q.1

Two parallel slits are illuminated by light of two wavelengths; one of which is 6 x 10 m ( ). On a screen the fourth ( ) dark line of the known wavelength coincides with the fifth ( ) bright line of the unknown wavelength. Calculate the unknown wavelength ( ).

-7

ARI F RAZA

.
Hint:-7 (4.2 x 10 m)
. /

/

(

)
1992

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NATURE OF LIGHT CHAPTER # 9 Q.2 th NUMERICALS

[e-mail] ) when the light of

If the radius of the 10 ( ) bright Newton’s ring is 0.5 mm ( -7 6.0 x 10 m ( ) is used, what is the radius of curvature ( ) of the lens used? Hint:√.
. /

/
( . / )

(√.

/

)

.

/

ARI F RAZA

Q.3

(43.85 x 10 m) 1994 Interference fringes were produced by two silts on a screen 0.8 m ( ) from them when the light of wavelength -7 5.8 x10 m ( ) was used. If the separation between the first and fifth bright fringe is 2.5 mm ( ); calculate the separation ( ) of two silts. ( ) ( ) ( ) ( ) Hint:( )

-3

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NATURE OF LIGHT CHAPTER # 9
-4

NUMERICALS

[e-mail]

Q.4

(7.424 x 10 m) 1995 Red light falls normally on diffraction grating ruled 4000 lines/cm ( ) and the 0 second order ( ) image is diffracted at 34 ( ) from the normal. Compute the wavelength ( ) of red light in angstroms.

ARI F RAZA

Q.5

Hint:-7 0 (6.98 x 10 m OR 6890 A ) 1996 th If the radius of the 14 ( ) bright Newton’s ring is 1.0 mm ( ) and the radius of curvature of the lens is 126 mm ( ), then calculate the wavelength ( ) of light. Page 100 of 111 “Not Only Is The Universe Stranger Than We Imagine, It Is Stranger Than We Can Imagine.” Arthur Eddington

NATURE OF LIGHT CHAPTER # 9 Hint:-7

NUMERICALS
√. / (√. / ) . /
( . / . / )

[e-mail]

Q.6

(5.878 x 10 m) 1997 How many fringes ( ) will pass a reference point if the moveable mirror of the Michelson’s Interferometer is moved by 0.8 mm ( )? The wavelength of light used is 0 ) 5800 A ( Hint:-

ARI F RAZA

Q.7

Q.8

Q.9

(2759) 1998 0 A green light of wavelength 5400 A ( ) is diffracted by a diffraction grating having 2000 lines/cm ( ). Compute the angular deviation ( ) of the third ( ) order. Hint:( ) 0 (18.90 ) 1998 th -7 If the radius of the 14 bright Newton’s ring is 1.0 mm when the light of wavelength 5.89 x 10 m is used. What is the radius of curvature of the lower surface of the lens used? Hint:- Same as Q.5 (125.7 mm) 1999 ) apart. If Interference fringes were produced by light coming from two silts 0.3 mm ( five ( ) fringes occupy 1.75 mm ( ) on a screen at 200 mm ( ) from the silts. Find the wavelength ( ) of light used. Hint:(5.25 x 10 m) 2000 th Determine the wavelength of a monochromatic light used if 14 bright Newton’s ring has a radius of 1 mm when a plano-convex of radius of curvature 126 mm is used. -7 (5.89 x 10 m) Hint:- Same a Q.5 2001 ) and the fringe In a double-slit experiment the separation of the silts is 1.8 mm ( ) mm at a distance of 1200 mm ( ) from the splits; find the spacing is 0.30 ( wavelength ( ) of the light used. Hint:-7 (4.5 x 10 m) 2002 P/E How much should the moveable mirror of the Michelson’s Interferometer be moved ( ) in order to obtain 400 ( ) fringes with reference to a point? The wavelength of the light used is 0 5890 A ( ) Page 101 of 111 “Not Only Is The Universe Stranger Than We Imagine, It Is Stranger Than We Can Imagine.” Arthur Eddington
-7

Q.10

Q.11

Q.12

NATURE OF LIGHT CHAPTER # 9

NUMERICALS

[e-mail]

Q.13

Q.14

Q.15

Q.16

Hint:-4 (1.178 x 10 m) 2002 P/E 271 ( ) fringes pass a reference point when the moveable mirror of the Michelson’s Interferometer is moved by 0.08 mm ( ). Find the wavelength ( ) of the light used in angstrom. Hint:0 (5904 A ) 2002 P/M th If the radius of the 12 ( ) dark Newton’s ring is 1mm ( ) when the light of wavelength 0 5890 A ( ) is used, what is the radius of curvature ( ) of the lower surface of the lens used? ( ) Hint:(√ ) √ (0.1414 m) 2003 P/E 0 When a light of wavelength 6000 A ( ) falls on diffraction grating, it produces 0 a second order ( ) spectrum at an angle of 30 ( ) from the normal. Find:(i) Grating element ( ); Hint:(ii) The number of lines/cm ( ) ruled on it. Hint:-6 (2.4 x 10 m, 4166 lines /cm) 2003 P/E th If the diameter of the 10 bright ( ) Newton’s ring is 0.005 m ( 0 ) when the light of wavelength 5893 A ( ) is used. What is the radius of curvature ( ) of the plano-convex lens? Also calculate the thickness ( ) of the air film corresponding to this ring.
ARI F RAZA

Hint:-

√. √

/ (√
-6

(√. )

/

)

.
(

/
)

( . / . /

)

Q.17

(1.116 m, 2.799 x 10 m) 0 X-rays of wavelength 1.54 A ( ) are diffracted by a crystal whose planes are 0 2.81 A ( ) apart. Find angle ( ) for the first order ( )? Hint:( )

2003 P/M

Q.18

(15.90 ) 0 A green light of wavelength 5400 A ( 2000 lines/cm ( Hint:- Same as Q.7 0 (18.90 )

0

2004 ) is diffracted by a grating of ). Find the angular deviation ( ) for the third order ( ). 2005 Page 102 of 111

“Not Only Is The Universe Stranger Than We Imagine, It Is Stranger Than We Can Imagine.” Arthur Eddington

NATURE OF LIGHT CHAPTER # 9 Q.19

NUMERICALS ).

[e-mail] ( ) at an angle of

Q.20

If a diffraction grating produces a first order ( ) spectrum of light of wavelength 0 20 ( ) from the normal, calculate the number of lines/mm ( Hint:(571 lines /mm) Interference fringes were produced by two silts 0.25 mm ( ) from the silts. If ten fringes ( ) occupy 3.275 mm ( 150 mm ( what is the wavelength ( ) of the light producing fringes? Hint:-7

2007 ) apart on a screen ),

Q.21

Q.22

Q.23

(5.458 x 10 m) 2008 A parallel beam of X-ray is diffracted by a crystal. The first order ( ) maximum is obtained when the glancing 0 angle of incidence is 6.5 ( ). If the distance between the atomic planes of the crystal is 0 2.8 A ( ). Calculate the wavelength ( ) of the radiation. Hint:-11 (6.33 x 10 m) 2009 th If the radius of the 14 bright Newton’s ring is 1.0 mm and the radius of curvature of the lens is 125 mm, then calculate the wavelength of light. Hint:- Same as Q.5 -7 (5.925 x 10 m) 2010 0 The green light of a wavelength 5400 A ( ) is diffracted by a grating of 2000 lines/cm ( ). Compute the angular deviation ( ) of the third order ( ) image. th Is the 10 ( ) order image possible? Hint:( )
ARI F RAZA

(

)

Q.24

(18.90 , not possible) If the diffraction grating produces first order ( ) spectrum of light of wavelength 0 20 ( ) from the normal, calculate the number of lines/mm ( Hint:- Same as Q.19 (571 lines /mm)

0

2010 ( ) at an angle of ). 2011

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GEOMETRICAL OPTICS CHAPTER # 10

QUESTIONS

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QUESTIONS

1992
Q.8 Write short notes on any of two following:(ii) Defect of lenses; (iv) Astronomical telescope.

1993
Q.7 Q.8 (b) Describe with the help of a ray diagram the image formed by a magnifying glass and expression for its magnification. Write short notes on any of two following:(iii) Defect of lenses; (iv) Compound microscope.

1994
Q.7 Q.7 Q. Q. Q. (a) What is visual angle? Explain the principle of magnifying glass. Calculate the magnifying power. (b) With the help of a ray diagram, calculate the magnifying power of a compound microscope. Fill in the blanks:(vi) In a telescope the focal length of the objective is greater than the focal length of the eye piece. True and false:(iv) The image formed by a convex lens for the different positions of the object is always real. (F) Choose the correct answer:(iv) The dispersion of white light in to seven different colors when passed through a prism is due to ___.  Different intensities  Different amplitudes  Different wavelengths  None of these (vi) When white light enters in to a denser medium its velocity ___.  Increases  Decreases  Remains the same  None of these
ARI F RAZA

1995
Q.7 Q. Write short notes on any of two following:(i) Thin lens formula for convex and concave lens; (iii) Astronomical telescope. Fill in the blanks:(ii) The size of the image formed by a concave lens is always less than the size of the object. (x) The least distance of distinct vision for a normal human eye is 25 cm. True and false:(xiii) The real images formed by a convex are always inverted and on the same side of the lens as the object. (F) (xx) It is not possible to photograph a virtual image. (T)

Q.

1996
Q.8 Fill in the blanks:(i) If an object is placed at focus of a converging lens its image will be formed at infinity. (ii) In a compound microscope the eye piece is used as a magnifying glass. Page 104 of 111 “If Nature Were Not Beautiful, It Would Not Be Worth Knowing, And If Nature Were Not Worth Knowing, Life Would Not Be Worth Living.” Henry Poincare (a)

GEOMETRICAL OPTICS CHAPTER # 10 Q.8 (b)

QUESTIONS

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Describe with the help of a neat diagram the construction and working of a compound microscope and hence derive the expression for its magnifying power.

1997
Q.7 (a) Fill in the blanks:(i) If an object is placed at the focus of a convex lens its image will be formed at infinity. (ii) The focal length of the eye piece of compound microscope is greater in comparison to the focal length of its objective. (iii) The crystalline lens of the human eye is convex. Two thin lenses with focal lengths “f1” and “f2” are placed together. Derive a formula for such system.

Q.7 Q.8

(b)

1998
Write short notes on any of two following:(i) Astronomical telescope; (ii) Defect of lenses; (iv) Thin lens formula; (v) Magnifying glass.

1999
Q.8 Write short notes on any of two following:(i) Compound microscope; (ii) Combination of thin lenses. Write short notes on any of two following:(i) Astronomical telescope; (ii) Magnifying glass.
ARI F RAZA

2000
Q.8

2001
Q.7 Q.8 (c) (a) Explain Chromatic and Spherical aberration in lenses and tell how they can be removed. Choose the correct answer:(iii) The power of a convex lens of the focal length 5 cm is ___.  1 diopter  5 diopters  20 diopters  0.2 diopter With the help of a ray diagram derive an expression for the magnifying power of a compound microscope. (Description of microscope is not required).

Q.8

(b)

2002 P/E
Q.7 Choose the correct answer:(iii) The power of a convex lens of the focal length 50 cm is ___.  0.5 diopter  2 diopters  0.02 diopter  50 diopters Q.7 (c) Explain Chromatic and Spherical aberration in lenses and tell how they can be removed. Q.8 (a) Choose the correct answer:(i) An astronomical telescope when focused for infinity with Fo= 60 cm and Fe= 3 cm has its focal length equals to ___  63 cm  20 cm  75 cm  180 cm Page 105 of 111 “If Nature Were Not Beautiful, It Would Not Be Worth Knowing, And If Nature Were Not Worth Knowing, Life Would Not Be Worth Living.” Henry Poincare (a)

GEOMETRICAL OPTICS CHAPTER # 10 (iii)

QUESTIONS

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Q.8 Q.7

(c) (a)

A defect of eye called myopia can be corrected by using the ___.  Convex lens  Concave lens  Bifocal lens  None of these What is a magnifying glass? Explain. Derive an expression for its magnification.

2002 P/M
Choose the correct answer:(iii) A student is wearing the glasses of power 25 diopters. This corresponds to the focal length of ___.  25 cm  60 cm  50 cm  40 cm Obtain the thin lens formula for convex lens. Choose the correct answer:(ii) Two convex lenses of same focal length “f” are kept touching each other. The focal length of the combination will be ___.  
ARI F RAZA

Q.7 Q.8

(b) (a)

Q.8

(c)

  Describe the construction and working of an astronomical telescope when it is focused for infinity. Draw ray diagram and obtain an expression for its magnifying power.

2003 P/E
Q.7 (a) Choose the correct answer:(ii) If a single convex lens is placed close to the eye, it is being used as ___.  Compound microscope  Telescope  Simple microscope  Spectrometer Describe the construction and working of a compound microscope with help of a ray diagram. Derive the expression for its magnifying power. Choose the correct answer:(i) The unit of the power of a lens is ___.  Watt  Joule  Diopter  Newton (iii) If an object is placed at 2F of a convex lens, the image will be formed at ___.  2F  4F  3F  F Two lenses of focal lengths “f1” and “f2” are placed in contact. Derive the formula for focal length of the combination.

Q.7 Q.8

(b) (a)

Q.8

(c)

2003 P/M
Q.7 Q.8 (b) (a) What are defect in the images formed by lenses? Explain. How they can be removed? Choose the correct answer:Page 106 of 111 “If Nature Were Not Beautiful, It Would Not Be Worth Knowing, And If Nature Were Not Worth Knowing, Life Would Not Be Worth Living.” Henry Poincare

GEOMETRICAL OPTICS CHAPTER # 10 (iii)

QUESTIONS

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Q.8

(c)

The magnifying power of a magnifying glass of focal length 25 cm is ___  0.5 Diopter  1 Diopter  0 diopter  2 diopters Describe the construction and working of a compound microscope. Derive an expression for its magnifying power.

2004
Q.7 Q.8 (c) (a) With the help of a ray diagram explain the working of a simple microscope. Derive the relation for its magnifying power. Choose the correct answer:(i) Chromatic aberration is caused by ___.  Reflection  Dispersion  Refraction  None of these (ii) The power of a concave lens of focal length 50 cm is ___.  0.5 diopter  -2 diopters  2 diopters  None of these Two thin convex lenses focal lengths “f1” and “f2” are placed in contact. Derive the formula for the focal length of their combination.
ARI F RAZA

Q.8

(c)

2005
Q.8 (a) Choose the correct answer:(i) The defect of lens which can be easily corrected by reducing its aperture is known as ___.  Spherical aberration  Astigmatism  Chromatic aberration  Hyperopia (ii) Two thin convex lenses each of focal length 10 cm are placed in contact with each other. Their equivalent focal length will be ___.  20 cm  10 cm  5 cm  100 cm What are defect in lenses? And how they can be removed? Draw a labeled diagram showing the passage of light rays through an astronomical telescope focused for infinity and obtain an expression for its magnifying power.

Q.8 Q.8

(b) (c)

2006
Q.7 Choose the correct answer:(i) If a single convex lens is placed close to an eye it is being used as ___.  Compound microscope  Telescope  Simple microscope  Spectrometer Q.7 (c) With the help of a ray diagram explain the working of a simple microscope. Derive the relation for its magnifying power. Q.8 (a) Choose the correct answer:(ii) In Galilean telescope, the final image formed is ___. Page 107 of 111 “If Nature Were Not Beautiful, It Would Not Be Worth Knowing, And If Nature Were Not Worth Knowing, Life Would Not Be Worth Living.” Henry Poincare (a)

GEOMETRICAL OPTICS CHAPTER # 10

QUESTIONS

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Q.8

(c)

 Real & inverted  Virtual and inverted  Real and erect  Virtual and erect (iii) If an astronomical telescope has an objective of local length 90 cm and the focal length of its eye piece 10 cm, the length of the telescope will be ___.  9 cm  100 cm  80 cm  None of these Draw a ray diagram of a compound microscope and derive the expression for its magnification. (Description is not required).

2007
Q.7 (a) Choose the correct answer:(ii) Chromatic aberration can be reduced by using a combination of ___.  Two converging lenses  Two diverging lenses  A converging lens and a diverging lens of different material  None of these Draw a neat ray diagram of a compound microscope and derive the expression for its magnification. (Description is not required0. Choose the correct answer:(iii) Two convex lenses of same focal length “f” are combined together. The focal length of the combined lens is ___.  
ARI F RAZA

Q.7 Q.8

(c) (a)

Q.8

(b)

   None of these Draw a labeled diagram showing the passage of light rays through astronomical telescope focused for infinity and obtained an expression for its magnifying power. (Description is not required).

2008
Q.7 (a) Choose the correct answer:(i) The power of a concave lens of focal length 50 cm is ___.  0.5 diopter  -0.5 diopter  2 diopters  -2 diopters Derive the lens formula for the convex lens. Choose the correct answer:(i) In Galilean telescope the final image formed is ___.  Real and inverted  Virtual and inverted  Real and erect  Virtual and erect (ii) In case of short-sightedness the image of an object is formed ___.  On the retina  In front of the of retina  Behind the retina  At the least distance of distinct vision

Q.7 Q.8

(c) (a)

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GEOMETRICAL OPTICS CHAPTER # 10 Q.8 Q.1 (b)

QUESTIONS

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What is a magnifying glass? Give its working and derive an expression for its magnifying power.

2009
Choose the correct answer for each from the given options:(xiii) Two convex lenses of same focal length “f” are kept in contact with each other. The focal length of the combined lens will be ___.  2f   Q.2 Q.3 (iv) (b)  f Why do thick lenses possesses Chromatic and Spherical aberrations? Suggest remedies for the rectification of these defects. With the help of a neat ray diagram describe the construction and working of a compound microscope. Derive the formula for its magnification.

2010
Q.1 Choose the correct answer for each from the given options:(vii) By using adjustable aperture of a lens we can reduce the defect of the lens called ___.  Astigmatism  Chromatic aberration  Spherical aberration  None of them (xiii) If the power of a converging lens is 4 diopters, what is the focal length of the lens?  20 cm  25 cm  10 cm  50 cm (iii) How is the magnifying power of a telescope and a microscope affected by increasing the focal lengths of their objectives?
ARI F RAZA

Q.2 Ans.

The magnifying power of a telescope is gives as:is given as:( ), here shorter the

, so increasing the

will increase the telescope magnification. For microscope it will become small and will become large

will increase the magnification because

making linear magnification large.

Q.3

(b)

What is magnifying power? Give its formula. With the help of a diagram describe the construction and working of an astronomical telescope and derive the formula for its magnification.

2011
Q.1 Select the most appropriate answer for each from the given options:(xi) The magnifying power of a lens of focal length 25 cm is ___.     With the help of a neat diagram, describe the construction and working of a compound microscope. Derive the formula for its magnification.

Q.5

(a)

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GEOMETRICAL OPTICS CHAPTER # 10

NUMERICALS

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Q.1 Define diopter. A lens has power +2 D (diopters). What do you know about the lens? ( ) Hint:( ) Q.2 (Focal length = 0.5 m) 1993 If a magnifying glass produces an image of magnification 6 ( ), what is the power of the lens ( )? What is the best position ( ) of the object? If the watch maker hold the same glass close to his eyes to see the damaged spring of a watch. Hint:- ( )
(

)

(

)
( )

( )

Q.3

() ( ) (20 diopters, 4.16 cm) 1993 The length of a compound microscope is 30 cm ( ). The focal length of the objective is 0.25 cm ( ) and that of the eye piece is 10 cm ( ). Calculate its magnifying power ( ) if the final image is formed at a distance of 250 mm ( ) from the eye piece. Hint:. / ( )
ARI F RAZA

( ( )( )

)

(

)(

)

( )

.

/

.

/

(

)

Q.4

Q.5

(323.92) 1994 In a compound microscope the focal lengths of the objective and the eye piece are 0.8 cm ( ) and 2.5 cm ( ) respectively. The real image formed by the objective is 16 cm ( ) from it. Determine the magnifying power ( ) of the microscope if the eye is held close to the eye piece and the image is formed at 25 cm ( ) from the eye piece. Hint:- Same as Q.3 (209) 1996 The focal length of a convex lens is 20 cm ( ), where should an object ( ) be placed so as to form an image double ( ) of the size of the object? Hint:( )( ) ( )( ) (30 cm) 1997 The magnifying power of a magnifying glass is 6. What is the power of lens in diopters? What is the best position of the object, if the watch maker hold the same glass close to his eyes to see the damaged spring of a watch?

Q.6

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GEOMETRICAL OPTICS CHAPTER # 10

NUMERICALS

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Q.7

(20 diopters, 4.16 cm) Hint:- Same as Q.2 2001 A telescope has the objective and eye piece lenses of power 2.0 ( ) and 20.0 diopters ( ) respectively. What is the magnifying power ( ) and length of the telescope ( ) if it is focused for infinity? Hint:(10, 55 cm) 2002 P/M A compound microscope has an objective and an eye piece of focal lengths 1 cm ( ) and 5 cm ( ) respectively. The object is located at a distance of 1.05 cm ( ) from the objective and forms an image 4.17 cm ( ) close to the eye piece; find the separation ( ) of the lenses and the magnifying power ( ) of the microscope. (25.17 cm, 120) 2003 P/M A magnifying glass of what power should be used to obtain an image of magnification 6? Hint:- Same as Q.2 (20) 2004 Two convex lenses of power 2 diopters ( ) and 20 diopters ( ) are used as an objective and eye piece of a telescope; find the magnifying power ( ) and length of the telescope ( ). Hint:- Same as Q.7 (10, 55 cm) 2005 A magnifying glass of what power should be used to obtain an image of magnification 6? Hint:- Same as Q.2 (20) 2006 A compound microscope has an objective of focal length 10 mm ( ) and a tube 100 mm ( ) long. An image is produced at 250 mm ( ) from the eye piece when the object is 12 mm ( ) from the objective. What is the angular magnification ( )? Hint:- Same as Q.3 (31.25) 2006 If the magnification of a telescope is 11 ( ) and its length is 120 cm ( ), determine the focal lengths of its objective ( ) and eye piece ( ) when the telescope is focused for infinity. ( ) ( ) Hint:ARI F RAZA

Q.8

Q.9

Q.10

Q.11

Q.12

Q.13

Q.14

Q.15

Q.16

(f1=110 cm, f2=10 cm) 2007 A compound microscope has an objective with a focal length of 10 mm ( ) and a tube 232 mm ( ) long. The final image is produced at 250 mm ( ) from the eye piece when the object is 10.5 mm ( ) from the objective. What is the angular magnification ( )? Hint:- Same as Q.3 (227) 2008 What is the magnification of an astronomical telescope, focused for infinity, when the powers of its objective and the eye-piece lenses are 2 diopters and 20 diopters respectively? Hint:- Same as Q.7 (10) 2009 A convex lens of power 4 diopters ( ) is in close combination with a concave lens of power 2 diopters ( ). Find the resultant power ( ) and the focal length ( ) of the combined lens system. ( ) Hint:(2 diopters. 50 cm) 2009 A magnifying glass produces an image of magnification 6. What is the power of the lens? What is the best position of the object if the watch maker hold the same lens close to his eye to see the damaged spring of the watch. Hint:- Same as Q.2 (20 diopters, 4.16 cm) 2010 Two converging lenses of focal lengths 30 cm ( ) and 60 cm ( ) are placed in contact. What is the focal length ( ) of this combination? Calculate the power ( ) of the combination in diopters. Hint:(20 cm, 5 diopters) 2011

Q.17

Q.18

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